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Seiberg Duality
In quantum field theory, Seiberg duality, conjectured by Nathan Seiberg in 1994, is an S-duality relating two different supersymmetric QCDs. The two theories are not identical, but they agree at low energies. More precisely under a renormalization group flow they flow to the same IR fixed point, and so are in the same universality class. It is an extension to nonabelian gauge theories with N=1 supersymmetry of Montonen–Olive duality in N=4 theories and electromagnetic duality in abelian theories. The statement of Seiberg duality Seiberg duality is an equivalence of the IR fixed points in an ''N''=1 theory with SU(Nc) as the gauge group and Nf flavors of fundamental chiral multiplets and Nf flavors of antifundamental chiral multiplets in the chiral limit (no bare masses) and an N=1 chiral QCD with Nf-Nc colors and Nf flavors, where Nc and Nf are positive integers satisfying ::N_f>N_c+1. A stronger version of the duality relates not only the chiral limit but also the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superconformal Algebra
In theoretical physics, the superconformal algebra is a graded Lie algebra or superalgebra that combines the conformal algebra and supersymmetry. In two dimensions, the superconformal algebra is infinite-dimensional. In higher dimensions, superconformal algebras are finite-dimensional and generate the superconformal group (in two Euclidean dimensions, the Lie superalgebra does not generate any Lie supergroup). Superconformal algebra in dimension greater than 2 The conformal group of the (p+q)-dimensional space \mathbb^ is SO(p+1,q+1) and its Lie algebra is \mathfrak(p+1,q+1). The superconformal algebra is a Lie superalgebra containing the bosonic factor \mathfrak(p+1,q+1) and whose odd generators transform in spinor representations of \mathfrak(p+1,q+1). Given Kač's classification of finite-dimensional simple Lie superalgebras, this can only happen for small values of p and q. A (possibly incomplete) list is * \mathfrak^*(2N, 2,2) in 3+0D thanks to \mathfrak(2,2)\simeq\math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moduli Space
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects. A variant of moduli spaces is formal moduli. Motivation Moduli spaces are spaces of solutions of geometric classification problems. That is, the points of a moduli space correspond to solutions of geometric problems. Here different solutions are identified if they a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Symmetry
In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be ''continuous'' (such as rotation of a circle) or ''discrete'' (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see '' Symmetry group''). These two concepts, Lie and finite groups, are the foundation for the fundamental theories of modern physics. Symmetries are frequently amenable to mathematical formulations such as group representations and can, in addition, be exploited to simplify many problems. Arguably the most important example of a symmetry in physics is that the speed of light has the same value in all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 groups). The term ''gauge'' refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called ''gauge transformations'', form a Lie group—referred to as the ''symmetry group'' or the ''gauge group'' of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the ''gauge field''. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called ''gauge invariance''). When such a theory is quantized, the quanta of the gauge fields are called ''gauge bosons' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 as fermions because they have half-integer spin. The name "baryon", introduced by Abraham Pais, comes from the Greek word for "heavy" (βαρύς, ''barýs''), because, at the time of their naming, most known elementary particles had lower masses than the baryons. Each baryon has a corresponding antiparticle (antibaryon) where their corresponding antiquarks replace quarks. For example, a proton is made of two up quarks and one down quark; and its corresponding antiparticle, the antiproton, is made of two up antiquarks and one down antiquark. Because they are composed of quarks, baryons participate in the strong interaction, which is mediated by particles known as gluons. The most familiar baryons are protons and neutrons, both of which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meson
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, they have a meaningful physical size, a diameter of roughly one femtometre (10 m), which is about 0.6 times the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond. Heavier mesons decay to lighter mesons and ultimately to stable electrons, neutrinos and photons. Outside the nucleus, mesons appear in nature only as short-lived products of very high-energy collisions between particles made of quarks, such as cosmic rays (high-energy protons and neutrons) and baryonic matter. Mesons are routinely produced artificially in cyclotrons or other particle accelerators in the collisions of protons, antiprotons, or other particles. Higher-energy (more massive) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Superconducting Model
In the theory of quantum chromodynamics, dual superconductor models attempt to explain confinement of quarks in terms of an electromagnetic dual theory of superconductivity. Overview In an electromagnetic dual theory the roles of electric and magnetic fields are interchanged. The BCS theory of superconductivity explains superconductivity as the result of the condensation of electric charges to Cooper pairs. In a dual superconductor an analogous effect occurs through the condensation of magnetic charges (also called magnetic monopoles). In ordinary electromagnetic theory, no monopoles have been shown to exist. However, in quantum chromodynamics — the theory of color charge which explains the strong interaction between quarks — the color charges can be viewed as (non-abelian) analogues of electric charges and corresponding magnetic monopoles are known to exist. Dual superconductor models posit that condensation of these magnetic monopoles in a superconductive state explains color ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colour Confinement
In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color-charged particles (such as quarks and gluons) cannot be isolated, and therefore cannot be directly observed in normal conditions below the Hagedorn temperature of approximately 2 terakelvin (corresponding to energies of approximately 130–140 MeV per particle). Quarks and gluons must clump together to form hadrons. The two main types of hadron are the mesons (one quark, one antiquark) and the baryons (three quarks). In addition, colorless glueballs formed only of gluons are also consistent with confinement, though difficult to identify experimentally. Quarks and gluons cannot be separated from their parent hadron without producing new hadrons. Origin There is not yet an analytic proof of color confinement in any non-abelian gauge theory. The phenomenon can be understood qualitatively by noting that the force-carrying gluons of QCD have color charge, unlike the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Higgs Phase
In theoretical physics, it is often important to consider gauge theory that admits many physical phenomena and "phases", connected by phase transitions, in which the vacuum may be found. Global symmetries in a gauge theory may be broken by the Higgs mechanism. In more general theories such as those relevant in string theory, there are often many Higgs fields that transform in different representations of the gauge group. If they transform in the adjoint representation or a similar representation, the original gauge symmetry is typically broken to a product of ''U(1)'' factors. Because ''U(1)'' describes electromagnetism including the Coulomb field, the corresponding phase is called a Coulomb phase. If the Higgs fields that induce the spontaneous symmetry breaking transform in other representations, the Higgs mechanism often breaks the gauge group completely and no ''U(1)'' factors are left. In this case, the corresponding vacuum expectation values describe a Higgs phase. Using t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
't Hooft–Polyakov Monopole
__NOTOC__ In theoretical physics, the t Hooft–Polyakov monopole is a topological soliton similar to the Dirac monopole but without the Dirac string. It arises in the case of a Yang–Mills theory with a gauge group G, coupled to a Higgs field which spontaneously breaks it down to a smaller group H via the Higgs mechanism. It was first found independently by Gerard 't Hooft and Alexander Polyakov. Unlike the Dirac monopole, the 't Hooft–Polyakov monopole is a smooth solution with a finite total energy. The solution is localized around r=0. Very far from the origin, the gauge group G is broken to H, and the 't Hooft–Polyakov monopole reduces to the Dirac monopole. However, at the origin itself, the G gauge symmetry is unbroken and the solution is non-singular also near the origin. The Higgs field :H_i \qquad (i=1,2,3) \, is proportional to :x_i f(, x, ) \, where the adjoint indices are identified with the three-dimensional spatial indices. The gauge field at infinity is suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 observable matter is composed of up quarks, down quarks and electrons. Owing to a phenomenon known as ''color confinement'', quarks are never found in isolation; they can be found only within hadrons, which include baryons (such as protons and neutrons) and mesons, or in quark–gluon plasmas. There is also the theoretical possibility of more exotic phases of quark matter. For this reason, much of what is known about quarks has been drawn from observations of hadrons. Quarks have various intrinsic properties, including electric charge, mass, color charge, and spin. They are the only elementary particles in the Standard Model of particle physics to experience all four fundamental interactions, also known as ''fundamental forces'' (electro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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