A Grand Unified Theory (GUT) is a model in
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
in which, at high
energies, the three
gauge interactions of the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
comprising the
electromagnetic,
weak
Weak may refer to:
Songs
* "Weak" (AJR song), 2016
* "Weak" (Melanie C song), 2011
* "Weak" (SWV song), 1993
* "Weak" (Skunk Anansie song), 1995
* "Weak", a song by Seether from '' Seether: 2002-2013''
Television episodes
* "Weak" (''Fear t ...
, and
strong
Strong may refer to:
Education
* The Strong, an educational institution in Rochester, New York, United States
* Strong Hall (Lawrence, Kansas), an administrative hall of the University of Kansas
* Strong School, New Haven, Connecticut, United S ...
forces are merged into a single force. Although this unified force has not been directly observed, many GUT models theorize its existence. If unification of these three interactions is possible, it raises the possibility that there was a
grand unification epoch in the
very early universe in which these three
fundamental interaction
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electro ...
s were not yet distinct.
Experiments have confirmed that at high energy the electromagnetic interaction and weak interaction unify into a single
electroweak interaction. GUT models predict that at even
higher energy, the strong interaction and the electroweak interaction will unify into a single electronuclear interaction. This interaction is characterized by one larger
gauge symmetry
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie group ...
and thus several
force carrier In quantum field theory, a force carrier, also known as messenger particle or intermediate particle, is a type of particle that gives rise to forces between other particles. These particles serve as the quanta of a particular kind of physical fi ...
s, but one unified
coupling constant
In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two ...
. Unifying
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
with the electronuclear interaction would provide a more comprehensive
theory of everything
A theory of everything (TOE or TOE/ToE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all asp ...
(TOE) rather than a Grand Unified Theory. Thus, GUTs are often seen as an intermediate step towards a TOE.
The novel particles predicted by GUT models are expected to have extremely high masses—around the
GUT scale of
GeV (just a few orders of magnitude below the
Planck scale of
GeV)—and so are well beyond the reach of any foreseen
particle hadron collider experiments. Therefore, the particles predicted by GUT models will be unable to be observed directly, and instead the effects of grand unification might be detected through indirect observations such as
proton decay
In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. The proton decay hypothesis was first formulated by Andrei Sakharov ...
,
electric dipole moment
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb- meter (C⋅m). ...
s of
elementary particle
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, ...
s, or the properties of
neutrino
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
s. Some GUTs, such as the
Pati–Salam model, predict the existence of
magnetic monopole
In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magneti ...
s.
While GUTs might be expected to offer simplicity over the complications present in the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
, realistic models remain complicated because they need to introduce additional fields and interactions, or even additional dimensions of space, in order to reproduce observed
fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
masses and mixing angles. This difficulty, in turn, may be related to an existence of
family symmetries In particle physics, the family symmetries or horizontal symmetries are various discrete, global, or local symmetries between quark-lepton families or generations. In contrast to the intrafamily or vertical symmetries (collected in the conventional ...
beyond the conventional GUT models. Due to this, and the lack of any observed effect of grand unification so far, there is no generally accepted GUT model.
Models that do not unify the three interactions using one
simple group as the gauge symmetry, but do so using
semisimple groups, can exhibit similar properties and are sometimes referred to as Grand Unified Theories as well.
History
Historically, the first true GUT which was based on the
simple Lie group , was proposed by
Howard Georgi and
Sheldon Glashow in 1974. The
Georgi–Glashow model was preceded by the
semisimple Lie algebra Pati–Salam model by
Abdus Salam
Mohammad Abdus Salam Salam adopted the forename "Mohammad" in 1974 in response to the anti-Ahmadiyya decrees in Pakistan, similarly he grew his beard. (; ; 29 January 192621 November 1996) was a Punjabis, Punjabi Pakistani theoretical physici ...
and
Jogesh Pati
Jogesh C. Pati (born 1937) is an Indian American theoretical physicist at the SLAC National Accelerator Laboratory.
Biography
Jogesh Pati started his schooling at Guru Training School, Baripada and then admitted to M.K.C High School where he ...
also in 1974, who pioneered the idea to unify gauge interactions.
The acronym GUT was first coined in 1978 by CERN researchers
John Ellis,
Andrzej Buras
Andrzej Jerzy Buras (Polish pronunciation: ; born 26 October 1946 in Warsaw, Poland) is a Polish-born Danish theoretical physicist, professor emeritus at the Technical University Munich (TUM).
Scientific career
He received his master's degree ...
,
Mary K. Gaillard, and
Dimitri Nanopoulos, however in the final version of their paper they opted for the less anatomical GUM (Grand Unification Mass). Nanopoulos later that year was the first to use the acronym in a paper.
Motivation
The ''supposition'' that the
electric charge
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons res ...
s of
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
s and
proton
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s seem to cancel each other exactly to extreme precision is essential for the existence of the macroscopic world as we know it, but this important property of elementary particles is not explained in the Standard Model of particle physics. While the description of
strong
Strong may refer to:
Education
* The Strong, an educational institution in Rochester, New York, United States
* Strong Hall (Lawrence, Kansas), an administrative hall of the University of Kansas
* Strong School, New Haven, Connecticut, United S ...
and
weak
Weak may refer to:
Songs
* "Weak" (AJR song), 2016
* "Weak" (Melanie C song), 2011
* "Weak" (SWV song), 1993
* "Weak" (Skunk Anansie song), 1995
* "Weak", a song by Seether from '' Seether: 2002-2013''
Television episodes
* "Weak" (''Fear t ...
interactions within the Standard Model is based on
gauge symmetries governed by the
simple symmetry groups and which allow only discrete charges, the remaining component, the
weak hypercharge interaction is described by an
abelian symmetry which in principle allows for arbitrary charge assignments.
[There are however certain constraints on the choice of particle charges from theoretical consistency, in particular anomaly cancellation.] The observed
charge quantization
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
, namely the postulation that all known
elementary particle
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, ...
s carry electric charges which are exact multiples of one-third of the
"elementary" charge, has led to the idea that
hypercharge interactions and possibly the strong and weak interactions might be embedded in one Grand Unified interaction described by a single, larger simple symmetry group containing the Standard Model. This would automatically predict the quantized nature and values of all elementary particle charges. Since this also results in a prediction for the relative strengths of the
fundamental interaction
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electro ...
s which we observe, in particular, the
weak mixing angle, grand unification ideally reduces the number of independent input parameters but is also constrained by observations.
Grand unification is reminiscent of the unification of electric and magnetic forces by
Maxwell's field theory of electromagnetism in the 19th century, but its physical implications and mathematical structure are qualitatively different.
Unification of matter particles
SU(5)
is the simplest GUT. The smallest
simple Lie group which contains the
standard model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
, and upon which the first Grand Unified Theory was based, is
:
.
Such group symmetries allow the reinterpretation of several known particles, including the photon, W and Z bosons, and gluon, as different states of a single particle field. However, it is not obvious that the simplest possible choices for the extended "Grand Unified" symmetry should yield the correct inventory of elementary particles. The fact that all currently known matter particles fit perfectly into three copies of the smallest
group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used ...
s of and immediately carry the correct observed charges, is one of the first and most important reasons why people believe that a Grand Unified Theory might actually be realized in nature.
The two smallest
irreducible representations of are (the defining representation) and . In the standard assignment, the contains the
charge conjugates of the right-handed
down-type quark color
Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are associ ...
triplet and a left-handed
lepton
In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
isospin
In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions ...
doublet, while the contains the six
up-type quark components, the left-handed
down-type quark color
Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are associ ...
triplet, and the right-handed
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
. This scheme has to be replicated for each of the three known
generations of matter. It is notable that the theory is
anomaly free with this matter content.
The hypothetical
right-handed neutrinos are a singlet of , which means its mass is not forbidden by any symmetry; it doesn't need a spontaneous electroweak symmetry breaking which explains why its mass would be heavy. (see
seesaw mechanism In the theory of grand unification of particle physics, and, in particular, in theories of neutrino masses and neutrino oscillation, the seesaw mechanism is a generic model used to understand the relative sizes of observed neutrino masses, of th ...
).
SO(10)
The next simple Lie group which contains the standard model is
:
.
Here, the unification of matter is even more complete, since the
irreducible spinor
In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a sligh ...
representation contains both the and of and a right-handed neutrino, and thus the complete particle content of one generation of the extended
standard model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
with
neutrino masses. This is already the largest
simple group that achieves the unification of matter in a scheme involving only the already known matter particles (apart from the
Higgs sector).
Since different standard model fermions are grouped together in larger representations, GUTs specifically predict relations among the fermion masses, such as between the
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
and the
down quark
The down quark or d quark (symbol: d) is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. Together with the up quark, it forms the neutrons (one up quark, two down quarks) and protons (two up ...
, the
muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As w ...
and the
strange quark
The strange quark or s quark (from its symbol, s) is the third lightest of all quarks, a type of elementary particle. Strange quarks are found in subatomic particles called hadrons. Examples of hadrons containing strange quarks include kaons ( ...
, and the
tau lepton and the
bottom quark for and . Some of these mass relations hold approximately, but most don't (see
Georgi-Jarlskog mass relation).
The boson matrix for is found by taking the matrix from the representation of and adding an extra row and column for the right-handed neutrino. The bosons are found by adding a partner to each of the 20 charged bosons (2 right-handed W bosons, 6 massive charged gluons and 12 X/Y type bosons) and adding an extra heavy neutral Z-boson to make 5 neutral bosons in total. The boson matrix will have a boson or its new partner in each row and column. These pairs combine to create the familiar 16D Dirac
spinor
In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a sligh ...
matrices of .
E6
In some forms of
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
, including E
8 × E
8 heterotic string theory
In string theory, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a superstring and a bosonic string. There are two kinds of heterotic string, the heterotic SO(32) and the heterotic E8 × E8, abbrevia ...
, the resultant four-dimensional theory after spontaneous
compactification on a six-dimensional
Calabi–Yau manifold
In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstrin ...
resembles a GUT based on the group
E6. Notably E
6 is the only
exceptional simple Lie group
In mathematics, a simple Lie group is a connected non-abelian Lie group ''G'' which does not have nontrivial connected normal subgroups. The list of simple Lie groups can be used to read off the list of simple Lie algebras and Riemannian sym ...
to have any
complex representation
In mathematics, a complex representation is a representation of a group (or that of Lie algebra) on a complex vector space. Sometimes (for example in physics), the term complex representation is reserved for a representation on a complex vector sp ...
s, a requirement for a theory to contain chiral fermions (namely all weakly-interacting fermions). Hence the other four (
G2,
F4,
E7, and
E8) can't be the gauge group of a GUT.
Extended Grand Unified Theories
Non-chiral extensions of the Standard Model with vectorlike split-multiplet particle spectra which naturally appear in the higher SU(N) GUTs considerably modify the desert physics and lead to the realistic (string-scale) grand unification for conventional three quark-lepton families even without using
supersymmetry
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
(see below). On the other hand, due to a new missing VEV mechanism emerging in the supersymmetric SU(8) GUT the simultaneous solution to the gauge hierarchy (doublet-triplet splitting) problem and problem of unification of flavor can be argued.
GUTs with four families / generations, SU(8): Assuming 4 generations of fermions instead of 3 makes a total of types of particles. These can be put into representations of . This can be divided into which is the theory together with some heavy bosons which act on the generation number.
GUTs with four families / generations, O(16): Again assuming 4 generations of fermions, the 128 particles and anti-particles can be put into a single spinor representation of .
Symplectic groups and quaternion representations
Symplectic gauge groups could also be considered. For example, (which is called in the article
symplectic group) has a representation in terms of quaternion unitary matrices which has a dimensional real representation and so might be considered as a candidate for a gauge group. has 32 charged bosons and 4 neutral bosons. Its subgroups include so can at least contain the gluons and photon of . Although it's probably not possible to have weak bosons acting on chiral fermions in this representation. A quaternion representation of the fermions might be:
:
A further complication with
quaternion
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quater ...
representations of fermions is that there are two types of multiplication: left multiplication and right multiplication which must be taken into account. It turns out that including left and right-handed quaternion matrices is equivalent to including a single right-multiplication by a unit quaternion which adds an extra SU(2) and so has an extra neutral boson and two more charged bosons. Thus the group of left- and right-handed quaternion matrices is which does include the standard model bosons:
:
If
is a quaternion valued spinor,
is quaternion hermitian matrix coming from and
is a pure imaginary quaternion (both of which are 4-vector bosons) then the interaction term is:
::
Octonion representations
It can be noted that a generation of 16 fermions can be put into the form of an
octonion
In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface or blackboard bold \mathbb O. Octonions hav ...
with each element of the octonion being an 8-vector. If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional (Grassmann)
Jordan algebra, which has the symmetry group of one of the exceptional Lie groups (F
4, E
6, E
7 or E
8) depending on the details.
:
:
Because they are fermions the anti-commutators of the Jordan algebra become commutators. It is known that E
6 has subgroup and so is big enough to include the Standard Model. An E
8 gauge group, for example, would have 8 neutral bosons, 120 charged bosons and 120 charged anti-bosons. To account for the 248 fermions in the lowest multiplet of E
8, these would either have to include anti-particles (and so have
baryogenesis
In physical cosmology, baryogenesis (also known as baryosynthesis) is the physical process that is hypothesized to have taken place during the early universe to produce baryonic asymmetry, i.e. the imbalance of matter (baryons) and antimatter (a ...
), have new undiscovered particles, or have gravity-like (
spin connection) bosons affecting elements of the particles spin direction. Each of these possesses theoretical problems.
Beyond Lie groups
Other structures have been suggested including
Lie 3-algebras and
Lie superalgebras. Neither of these fit with
Yang–Mills theory
In mathematical physics, Yang–Mills theory is a gauge theory based on a special unitary group SU(''N''), or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using t ...
. In particular Lie superalgebras would introduce bosons with incorrect statistics.
Supersymmetry
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
, however, does fit with Yang–Mills.
Unification of forces and the role of supersymmetry
The unification of forces is possible due to the energy scale dependence of force
coupling parameters in
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
called
renormalization group "running", which allows parameters with vastly different values at usual energies to converge to a single value at a much higher energy scale.
The
renormalization group
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in t ...
running of the three gauge couplings in the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
has been found to nearly, but not quite, meet at the same point if the
hypercharge is normalized so that it is consistent with or GUTs, which are precisely the GUT groups which lead to a simple fermion unification. This is a significant result, as other Lie groups lead to different normalizations. However, if the
supersymmetric extension
MSSM is used instead of the Standard Model, the match becomes much more accurate. In this case, the coupling constants of the strong and electroweak interactions meet at the
grand unification energy, also known as the GUT scale:
:
.
It is commonly believed that this matching is unlikely to be a coincidence, and is often quoted as one of the main motivations to further investigate
supersymmetric theories despite the fact that no supersymmetric partner particles have been experimentally observed. Also, most model builders simply assume
supersymmetry
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
because it solves the
hierarchy problem
In theoretical physics, the hierarchy problem is the problem concerning the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 1024 times stronger than grav ...
—i.e., it stabilizes the electroweak
Higgs mass against
radiative corrections.
Neutrino masses
Since
Majorana masses of the right-handed neutrino are forbidden by symmetry, GUTs predict the Majorana masses of right-handed neutrinos to be close to the
GUT scale where the symmetry is
spontaneously broken
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the ...
in those models. In
supersymmetric GUTs, this scale tends to be larger than would be desirable to obtain realistic masses of the light, mostly left-handed neutrinos (see
neutrino oscillation) via the
seesaw mechanism In the theory of grand unification of particle physics, and, in particular, in theories of neutrino masses and neutrino oscillation, the seesaw mechanism is a generic model used to understand the relative sizes of observed neutrino masses, of th ...
. These predictions are independent of the
Georgi–Jarlskog mass relations, wherein some GUTs predict other fermion mass ratios.
Proposed theories
Several theories have been proposed, but none is currently universally accepted. An even more ambitious theory that includes ''all''
fundamental forces
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electro ...
, including
gravitation
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
, is termed a
theory of everything
A theory of everything (TOE or TOE/ToE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all asp ...
. Some common mainstream GUT models are:
*
Pati–Salam model —
*
Georgi–Glashow model — ; and
Flipped —
*
SO(10) model; and
Flipped —
*
E6 model; and
Trinification —
* minimal
left-right model —
*
331 model
The 331 model in particle physics is an extension of the electroweak gauge symmetry which offers an explanation of why there must be three families of quarks and leptons. The name "331" comes from the full gauge symmetry group SU(3)_C \tim ...
—
*
chiral color
In particle physics phenomenology, chiral color is a speculative model which extends quantum chromodynamics (QCD), the generally accepted theory for the strong interactions of quarks. QCD is a gauge field theory based on a gauge group known as co ...
Not quite GUTs:
*
Technicolor models
*
Little Higgs
*
String theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
*
Causal fermion system
The theory of causal fermion systems is an approach to describe fundamental physics. It provides a unification of the weak, the strong and the electromagnetic forces with gravity at the level of classical field theory. Moreover, it gives q ...
s
*
M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's ...
*
Preon
In particle physics, preons are point particles, conceived of as sub-components of quarks and leptons.
The word was coined by Jogesh Pati and Abdus Salam, in 1974. Interest in preon models peaked in the 1980s but has slowed, as the Standard Mode ...
s
*
Loop quantum gravity
*
Causal dynamical triangulation theory
''Note'': These models refer to
Lie algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...
s not to
Lie group
In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...
s. The Lie group could be , just to take a random example.
The most promising candidate is . (Minimal) does not contain any
exotic fermion
Exotic may refer to:
Mathematics and physics
* Exotic R4, a differentiable 4-manifold, homeomorphic but not diffeomorphic to the Euclidean space R4
*Exotic sphere, a differentiable ''n''-manifold, homeomorphic but not diffeomorphic to the ordinar ...
s (i.e. additional fermions besides the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
fermions and the right-handed neutrino), and it unifies each generation into a single
irreducible representation
In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation (\rho, V) or irrep of an algebraic structure A is a nonzero representation that has no proper nontrivial subrepresentation (\rho, _W,W ...
. A number of other GUT models are based upon subgroups of . They are the minimal
left-right model, ,
flipped and the
Pati–Salam model. The GUT group E
6 contains , but models based upon it are significantly more complicated. The primary reason for studying E
6 models comes from
heterotic string theory
In string theory, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a superstring and a bosonic string. There are two kinds of heterotic string, the heterotic SO(32) and the heterotic E8 × E8, abbrevia ...
.
GUT models generically predict the existence of
topological defect
A topological soliton occurs when two adjoining structures or spaces are in some way "out of phase" with each other in ways that make a seamless transition between them impossible. One of the simplest and most commonplace examples of a topological ...
s such as
monopoles,
cosmic strings
Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simp ...
,
domain wall
A domain wall is a type of topological soliton that occurs whenever a discrete symmetry is spontaneously broken. Domain walls are also sometimes called kinks in analogy with closely related kink solution of the sine-Gordon model or models with pol ...
s, and others. But none have been observed. Their absence is known as the
monopole problem
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularit ...
in
cosmology
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in ...
. Many GUT models also predict
proton decay
In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. The proton decay hypothesis was first formulated by Andrei Sakharov ...
, although not the Pati–Salam model. As of now, proton decay has never been experimentally observed. The minimal experimental limit on the proton's lifetime pretty much rules out minimal and heavily constrains the other models. The lack of detected supersymmetry to date also constrains many models.
X bosons and Higgs boson
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field,
one of the fields in particle physics theory. In the Stand ...
s." widths="250px" heights="300px" perrow="3">
File:Proton_decay2.svg, Dimension 6 proton decay mediated by the ''X'' boson in GUT
File:proton decay3.svg, Dimension 6 proton decay mediated by the ''X'' boson in flipped GUT
File:proton decay4.svg, Dimension 6 proton decay mediated by the triplet Higgs and the anti-triplet Higgs in GUT
Some GUT theories like and suffer from what is called the
doublet-triplet problem. These theories predict that for each electroweak Higgs doublet, there is a corresponding
colored
''Colored'' (or ''coloured'') is a racial descriptor historically used in the United States during the Jim Crow, Jim Crow Era to refer to an African Americans, African American. In many places, it may be considered a Pejorative, slur, though it ...
Higgs triplet field with a very small mass (many orders of magnitude smaller than the GUT scale here). In theory, unifying
quark
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly o ...
s with
lepton
In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
s, the Higgs doublet would also be unified with a Higgs triplet. Such triplets have not been observed. They would also cause extremely rapid proton decay (far below current experimental limits) and prevent the gauge coupling strengths from running together in the renormalization group.
Most GUT models require a threefold replication of the matter fields. As such, they do not explain why there are three generations of fermions. Most GUT models also fail to explain the
little hierarchy between the fermion masses for different generations.
Ingredients
A GUT model consists of a
gauge group
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations ( Lie group ...
which is a
compact Lie group
In mathematics, a compact (topological) group is a topological group whose topology realizes it as a compact topological space (when an element of the group is operated on, the result is also within the group). Compact groups are a natural gene ...
, a
connection form In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms.
Historically, connection forms were introduced by Élie Carta ...
for that Lie group, a
Yang–Mills action for that connection given by an
invariant
Invariant and invariance may refer to:
Computer science
* Invariant (computer science), an expression whose value doesn't change during program execution
** Loop invariant, a property of a program loop that is true before (and after) each iteratio ...
symmetric bilinear form In mathematics, a symmetric bilinear form on a vector space is a bilinear map from two copies of the vector space to the field of scalars such that the order of the two vectors does not affect the value of the map. In other words, it is a bilinear ...
over its Lie algebra (which is specified by a
coupling constant
In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two ...
for each factor), a
Higgs sector In particle physics, the Higgs sector is the collection of quantum fields and/or particles that are responsible for the Higgs mechanism, i.e. for the spontaneous symmetry breaking of the Higgs field
The Higgs boson, sometimes called the Higg ...
consisting of a number of scalar fields taking on values within real/complex
representations
''Representations'' is an interdisciplinary journal in the humanities published quarterly by the University of California Press. The journal was established in 1983 and is the founding publication of the New Historicism movement of the 1980s. It ...
of the Lie group and chiral
Weyl fermion
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is ...
s taking on values within a complex rep of the Lie group. The Lie group contains the
Standard Model group Standard may refer to:
Symbols
* Colours, standards and guidons, kinds of military signs
* Standard (emblem), a type of a large symbol or emblem used for identification
Norms, conventions or requirements
* Standard (metrology), an object t ...
and the Higgs fields acquire
VEV
In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle. ...
s leading to a
spontaneous symmetry breaking
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the ...
to the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
. The Weyl fermions represent matter.
Current status
There is currently no hard evidence that nature is described by a Grand Unified Theory. The discovery of
neutrino oscillations indicates that the Standard Model is incomplete and has led to renewed interest toward certain GUT such as . One of the few possible experimental tests of certain GUT is
proton decay
In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. The proton decay hypothesis was first formulated by Andrei Sakharov ...
and also fermion masses. There are a few more special tests for supersymmetric GUT. However, minimum proton lifetimes from research (at or exceeding the 10
34-10
35 year range) have ruled out simpler GUTs and most non-SUSY models. The maximum upper limit on proton lifetime (if unstable), is calculated at 6 x 10
39 years for SUSY models and 1.4 x 10
36 years for minimal non-SUSY GUTs.
The
gauge coupling strengths of
QCD
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a ty ...
, the
weak interaction
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, ...
and
hypercharge seem to meet at a common length scale called the
GUT scale The grand unification energy \Lambda_, or the GUT scale, is the energy level above which, it is believed, the electromagnetic force, weak force, and strong force become equal in strength and unify to one force governed by a simple Lie group. The exa ...
and equal approximately to 10
16 GeV (slightly less than the
Planck energy of 10
19 GeV), which is somewhat suggestive. This interesting numerical observation is called the gauge coupling unification, and it works particularly well if one assumes the existence of
superpartner
In particle physics, a superpartner (also sparticle) is a class of hypothetical elementary particles predicted by supersymmetry, which, among other applications, is one of the well-studied ways to extend the standard model of high-energy physics.
...
s of the Standard Model particles. Still it is possible to achieve the same by postulating, for instance, that ordinary (non supersymmetric) models break with an intermediate gauge scale, such as the one of Pati–Salam group.
Ultra unification
In 2020, a proposed theory called "ultra unification"
would combine the Standard Model and grand unification, particularly for the models with 15 Weyl fermions per generation, without the necessity of right-handed sterile
neutrinos
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is ...
by adding new gapped topological phase sectors consistent with the nonperturbative
global anomaly
In theoretical physics, a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformation that would otherwise be preserved in the classical theory. This leads to an inconsistenc ...
cancellation and
cobordism
In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French '' bord'', giving ''cobordism'') of a manifold. Two manifolds of the same dim ...
constraints (especially from the
baryon
In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classified ...
minus
lepton
In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
number
B−L, the
electroweak hypercharge Y, and the mixed gauge-gravitational
anomaly such as a Z/''16''Z class anomaly). Gapped topological phase sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant
topological quantum field theories
In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.
Although TQFTs were invented by physicists, they are also of mathem ...
(TQFTs), such as four dimensional noninvertible, five dimensional noninvertible, or five dimensional invertible entangled gapped phase TQFTs. Alternatively, there could also be right-handed sterile
neutrinos
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is ...
, gapless
unparticle
In theoretical physics, unparticle physics is a speculative theory that conjectures a form of matter that cannot be explained in terms of particles using the Standard Model of particle physics, because its components are scale invariant.
Howard ...
physics, or some combination of more general interacting
conformal field theories
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometime ...
, to cancel the mixed gauge-gravitational
anomaly. In either case, this implies a new high-energy physics frontier beyond the conventional zero dimensional
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
that relies on new types of topological forces and matter, including gapped extended objects such as line and surface operators or conformal defects, whose open ends carry deconfined fractionalized particle or
anyonic string excitations. A physical characterization of these gapped extended objects require extensions of mathematical concepts such as
cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...
,
cobordism
In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French '' bord'', giving ''cobordism'') of a manifold. Two manifolds of the same dim ...
, or
categories
Category, plural categories, may refer to:
Philosophy and general uses
*Categorization, categories in cognitive science, information science and generally
*Category of being
*Categories (Aristotle), ''Categories'' (Aristotle)
*Category (Kant)
...
into particle physics.
See also
*
B − L
In high-energy physics, ''B'' − ''L'' (pronounced "bee minus ell") is the difference between the baryon number (''B'') and the lepton number (''L'').
Details
This quantum number is the charge of a global/gauge U(1) symmetry in so ...
quantum number
*
Classical unified field theories
Since the 19th century, some physicists, notably Albert Einstein, have attempted to develop a single theoretical framework that can account for all the fundamental forces of nature – a unified field theory. Classical unified field theories are at ...
*
Paradigm shift
A paradigm shift, a concept brought into the common lexicon by the American physicist and philosopher Thomas Kuhn, is a fundamental change in the basic concepts and experimental practices of a scientific discipline. Even though Kuhn restricted t ...
*
Physics beyond the Standard Model
*
Theory of everything
A theory of everything (TOE or TOE/ToE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all asp ...
*
X and Y bosons
In particle physics, the X and Y bosons (sometimes collectively called "X bosons"
) are hypothetical elementary particles analogous to the W and Z bosons, but corresponding to a unified force predicted by the Georgi–Glashow model, a grand unifi ...
Notes
References
Further reading
*
Stephen Hawking,
A Brief History of Time
''A Brief History of Time: From the Big Bang to Black Holes'' is a book on theoretical cosmology by English physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for readers who had no prior knowledge of physics.
I ...
, includes a brief popular overview.
*
External links
The Algebra of Grand Unified Theories
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Particle physics
Physical cosmology
Physics beyond the Standard Model