Super QCD

Last updated

In theoretical physics, super QCD is a supersymmetric gauge theory which resembles quantum chromodynamics (QCD) but contains additional particles and interactions which render it supersymmetric.

The most commonly used version of super QCD is in 4 dimensions and contains one Majorana spinor supercharge. The particle content consists of vector supermultiplets, which include gluons and gluinos and also chiral supermultiplets which contain quarks and squarks transforming in the fundamental representation of the gauge group. This theory has many features in common with real world QCD, for example in some phases it manifests confinement and chiral symmetry breaking. The supersymmetry of this theory means that, unlike QCD, one may use nonrenormalization theorems to analytically demonstrate the existence of these phenomena and even calculate the condensate which breaks the chiral symmetry.

Phases of super QCD

Consider 4-dimensional SQCD with gauge group SU(N) and M flavors of chiral multiplets. The vacuum structure depends on M and N. The (spin-zero) squarks may be reorganized into hadrons, and the moduli space of vacua of the theory may be parametrized by their vacuum expectation values. On most of the moduli space the Higgs mechanism makes all of the fields massive, and so they may be integrated out. Classically, the resulting moduli space is singular. The singularities correspond to points where some gluons are massless, and so could not be integrated out. In the full quantum moduli space is nonsingular, and its structure depends on the relative values of M and N. For example, when M is less than or equal to N+1, the theory exhibits confinement.

When M is less than N, the effective action differs from the classical action. More precisely, while the perturbative nonrenormalization theory forbids any perturbative correction to the superpotential, the superpotential receives nonperturbative corrections. When N=M+1, these corrections result from a single instanton. For larger values of N the instanton calculation suffers from infrared divergences, however the correction may nonetheless be determined precisely from the gaugino condensation. The quantum correction to the superpotential was calculated in The Massless Limit Of Supersymmetric Qcd. If the chiral multiplets are massless, the resulting potential energy has no minimum and so the full quantum theory has no vacuum. Instead the fields roll forever to larger values.

When M is equal to or greater than N, the classical superpotential is exact. When M is equal to N, however, the moduli space receives quantum corrections from a single instanton. This correction renders the moduli space nonsingular, and also leads to chiral symmetry breaking. Then M is equal to N+1 the moduli space is not modified and so there is no chiral symmetry breaking, however there is still confinement.

When M is greater than N+1 but less than 3N/2, the theory is asymptotically free. However at low energies the theory becomes strongly coupled, and is better described by a Seiberg dual description in terms of magnetic variables with the same global flavor symmetry group but a new gauge symmetry SU(M-N). Notice that the gauge group is not an observable, but simply reflects the redundancy or a description and so may well differ in various dual theories, as it does in this case. On the other hand, the global symmetry group is an observable so it is essential that it is the same, SU(M), in both descriptions. The dual magnetic theory is free in the infrared, the coupling constant shrinks logarithmically, and so by the Dirac quantization condition the electric coupling constant grows logarithmically in the infrared. This implies that the potential between two electric charges, at long distances, scales as the logarithm of their distance divided by the distance.

When M is between 3N/2 and 3N, in the theory has an infrared fixed point where it becomes a nontrivial conformal field theory. The potential between electric charges obeys the usual Colomb law, it is inversely proportional to the distance between the charges.

When M is greater than 3N, the theory is free in the infrared, and so the force between two charges is inversely proportional to the product of the distance times the logarithm of the distance between the charges. However the theory is ill-defined in the ultraviolet, unless one includes additional heavy degrees of freedom which lead, for example, to a Seiberg dual theory of the type described above at N+1<M<3N/2.

Related Research Articles

Quantum chromodynamics Theory of the strong nuclear interactions

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 type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.

Instanton Solitons in Euclidean spacetime

An instanton is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime.

Nathan Seiberg

Nathan "Nati" Seiberg is an Israeli American theoretical physicist who works on quantum field theory and string theory. He is currently a professor at the Institute for Advanced Study in Princeton, New Jersey, United States.

In theoretical physics, a supermultiplet is a representation of a supersymmetry algebra.

In quantum field theory, the term moduli is sometimes used to refer to scalar fields whose potential energy function has continuous families of global minima. Such potential functions frequently occur in supersymmetric systems. The term "modulus" is borrowed from mathematics, where it is used synonymously with "parameter". The word moduli first appeared in 1857 in Bernhard Riemann's celebrated paper "Theorie der Abel'schen Functionen".

The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by non-vanishing condensates such as the gluon condensate and the quark condensate in the complete theory which includes quarks. The presence of these condensates characterizes the confined phase of quark matter.

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.

In theoretical physics, the Wess–Zumino model has become the first known example of an interacting four-dimensional quantum field theory with linearly realised supersymmetry. In 1974, Julius Wess and Bruno Zumino studied, using modern terminology, dynamics of a single chiral superfield whose cubic superpotential leads to a renormalizable theory.

Erick J. Weinberg is a theoretical physicist and professor of physics at Columbia University.

In theoretical physics, topological string theory is a version of string theory. Topological string theory appeared in papers by theoretical physicists, such as Edward Witten and Cumrun Vafa, by analogy with Witten's earlier idea of topological quantum field theory.

In theoretical physics, Seiberg–Witten theory is a theory that determines an exact low-energy effective action of a supersymmetric gauge theory—namely the metric of the moduli space of vacua.

The J. J. Sakurai Prize for Theoretical Particle Physics, is presented by the American Physical Society at its annual April Meeting, and honors outstanding achievement in particle physics theory. The prize consists of a monetary award, a certificate citing the contributions recognized by the award, and a travel allowance for the recipient to attend the presentation. The award is endowed by the family and friends of particle physicist J. J. Sakurai. The prize has been awarded annually since 1985.

In theoretical physics, the anti-de Sitter/quantum chromodynamics correspondence is a goal to describe quantum chromodynamics (QCD) in terms of a dual gravitational theory, following the principles of the AdS/CFT correspondence in a setup where the quantum field theory is not a conformal field theory.

In quantum field theory, the anomaly matching condition by Gerard 't Hooft states that the calculation of any chiral anomaly for the flavor symmetry must not depend on what scale is chosen for the calculation if it is done by using the degrees of freedom of the theory at some energy scale. It is also known as the 't Hooft condition and the 't Hooft UV-IR anomaly matching condition.

In mathematics, and especially gauge theory, Seiberg–Witten invariants are invariants of compact smooth oriented 4-manifolds introduced by Edward Witten (1994), using the Seiberg–Witten theory studied by Nathan Seiberg and Witten during their investigations of Seiberg–Witten gauge theory.

In theoretical physics a nonrenormalization theorem is a limitation on how a certain quantity in the classical description of a quantum field theory may be modified by renormalization in the full quantum theory. Renormalization theorems are common in theories with a sufficient amount of supersymmetry, usually at least 4 supercharges.

Higher-dimensional supergravity is the supersymmetric generalization of general relativity in higher dimensions. Supergravity can be formulated in any number of dimensions up to eleven. This article focuses upon supergravity (SUGRA) in greater than four dimensions.

This page is a glossary of terms in string theory, including related areas such as supergravity, supersymmetry, and high energy physics.

N = 4 supersymmetric Yang–Mills (SYM) theory is a mathematical and physical model created to study particles through a simple system, similar to string theory, with conformal symmetry. It is a simplified toy theory based on Yang–Mills theory that does not describe the real world, but is useful because it can act as a proving ground for approaches for attacking problems in more complex theories. It describes a universe containing boson fields and fermion fields which are related by 4 supersymmetries. It is one of the simplest and one of the few finite quantum field theories in 4 dimensions. It can be thought of as the most symmetric field theory that does not involve gravity.

In theoretical physics, 3D mirror symmetry is a version of mirror symmetry in 3-dimensional gauge theories with N=4 supersymmetry, or 8 supercharges. It was first proposed by Kenneth Intriligator and Nathan Seiberg, in their 1996 paper "Mirror symmetry in three-dimensional gauge theories", as a relation between pairs of 3-dimensional gauge theories, such that the Coulomb branch of the moduli space of one is the Higgs branch of the moduli space of the other. It was demonstrated using D-brane cartoons by Amihay Hanany and Edward Witten 4 months later, where they found that it is a consequence of S-duality in type IIB string theory.

References

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.