The Flipped SU(5) model is a
grand unified theory
A Grand Unified Theory (GUT) is a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this ...
(GUT) first contemplated by
Stephen Barr
__NOTOC__
Stephen Matthew Barr (born November 28, 1953) is an American physicist who is a professor emeritus of physics at the University of Delaware. A member of its Bartol Research Institute, Barr does research in theoretical particle physics a ...
in 1982, and by
Dimitri Nanopoulos
Dimitri V. Nanopoulos (; el, Δημήτρης Νανόπουλος; born 13 September 1948) is a Greek physicist. He is one of the most regularly cited researchers in the world, cited more than 48,500 times across a number of separate branches of ...
and others in 1984. Ignatios Antoniadis,
John Ellis,
John Hagelin
John Samuel Hagelin (born June 9, 1954) is the leader of the Transcendental Meditation (TM) movement in the United States. He is president of the Maharishi University of Management (MUM) in Fairfield, Iowa, and honorary chair of its board of tr ...
, and
Dimitri Nanopoulos
Dimitri V. Nanopoulos (; el, Δημήτρης Νανόπουλος; born 13 September 1948) is a Greek physicist. He is one of the most regularly cited researchers in the world, cited more than 48,500 times across a number of separate branches of ...
developed the supersymmetric flipped SU(5), derived from the deeper-level superstring.
Some current efforts to explain the theoretical underpinnings for observed neutrino masses are being developed in the context of supersymmetric flipped .
Flipped is not a fully unified model, because the factor of the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions - excluding gravity) in the universe and classifying a ...
gauge group is within the factor of the GUT group. The addition of states below ''M''x in this model, while solving certain threshold correction issues in
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 interac ...
, makes the model merely descriptive, rather than predictive.
Barcow, Timothy ''et al.'', ''Electroweak symmetry breaking and new physics at the TeV scale''
World Scientific, 1996, 194.
The model
The flipped model states that the 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 ...
is:
:
Fermions form three families, each consisting of the 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 ...
: for the lepton doublet, L, and the up quarks ;
: for the quark doublet, Q, the down quark, and the right-handed neutrino, ;
: for the charged leptons, .
This assignment includes three right-handed neutrinos, which have never been observed, but are often postulated to explain the lightness of the observed neutrinos and neutrino oscillations. There is also a and/or called the Higgs fields which acquire a 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. ...
, yielding the 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 ...
:
The representations transform under this subgroup as the reducible representation as follows:
: (uc and l)
: (q, dc and νc)
: (ec)
:.
Comparison with the standard SU(5)
The name "flipped" arose in comparison to the "standard" Georgi–Glashow model
In particle physics, the Georgi–Glashow model is a particular grand unified theory (GUT) proposed by Howard Georgi and Sheldon Glashow in 1974. In this model the standard model gauge groups SU(3) × SU(2) × U(1) are combined into a single ...
, in which and quark are respectively assigned to the and representation. In comparison with the standard , the flipped can accomplish the spontaneous symmetry breaking using Higgs fields of dimension 10, while the standard requires both a 5- and 45-dimensional Higgs.
The sign convention
In physics, a sign convention is a choice of the physical significance of signs (plus or minus) for a set of quantities, in a case where the choice of sign is arbitrary. "Arbitrary" here means that the same physical system can be correctly describ ...
for varies from article/book to article.
The hypercharge Y/2 is a linear combination (sum) of the following:
:
There are also the additional fields and containing the electroweak
In particle physics, the electroweak interaction or electroweak force is the unified field theory, unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two force ...
Higgs doublet
Higgs may refer to:
Physics
*Higgs boson, an elementary particle
*Higgs mechanism, an explanation for electroweak symmetry breaking
*Higgs field, a quantum field
People
*Alan Higgs (died 1979), English businessman and philanthropist
*Blaine Higgs ...
s.
Calling the 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 ...
for example, and is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableau In mathematics, a Young tableau (; plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus. It provides a convenient way to describe the group representations of the symmetric and general linear groups a ...
x or Dynkin diagram
In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise in the classification of semisimple Lie algebras ...
s with numbers on their vertices, and is a standard used by GUT
theorists.
Since the homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted \pi_1(X), which records information about loops in a space. Intuitively, homotop ...
:
this model does not predict monopoles. See 't Hooft–Polyakov monopole.
Minimal supersymmetric flipped SU(5)
Spacetime
The superspace extension of Minkowski spacetime
Spatial symmetry
SUSY over Minkowski spacetime with R-symmetry
In theoretical physics, the R-symmetry is the symmetry transforming different supercharges in a theory with supersymmetry into each other. In the simplest case of the ''N''=1 supersymmetry, such an R-symmetry is isomorphic to a global U(1) group o ...
Gauge symmetry group
Global internal symmetry
(matter parity) not related to in any way for this particular model
Vector superfields
Those associated with the gauge symmetry
Chiral superfields
As complex representations:
Superpotential
A generic invariant renormalizable superpotential is a (complex) invariant cubic polynomial in the superfields which has an -charge of 2. It is a linear combination of the following terms:
The second column expands each term in index notation (neglecting the proper normalization coefficient). and are the generation indices. The coupling has coefficients which are symmetric in and .
In those models without the optional sterile neutrinos, we add the nonrenormalizable
Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similarity, self-similar geometric structures, that are used to treat infinity, infinities arising in calculated ...
couplings instead.
These couplings do break the R-symmetry.
See also
* Flipped SO(10)
References
{{DEFAULTSORT:Flipped Su(5)
Grand Unified Theory