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{{Short description|A supersymmetric generalization of quantum chromodynamics}}
In [[theoretical physics]], '''super QCD''' is a [[supersymmetric gauge theory]] which resembles [[quantum chromodynamics]] (QCD) but contains additional particles and interactions which render it [[supersymmetry|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 superfield|vector supermultiplets]], which include [[gluon]]s and [[gluino]]s and also [[chiral superfield|chiral supermultiplets]] which contain [[quark]]s and [[squark]]s 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 [[color confinement|confinement]] and [[chiral symmetry breaking]]. The supersymmetry of this theory means that, unlike QCD, one may use [[nonrenormalization theorem]]s to analytically demonstrate the existence of these phenomena and even calculate the [[vacuum expectation value|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 [[vacuum|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 [[line integral|integrated out]]. Classically, the resulting moduli space is [[Mathematical singularity|singular]]. The singularities correspond to points where some gluons are massless, and so could not be integrated out. In the full [[quantum field theory|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 (physics)|action]]. More precisely, while the [[perturbation theory|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 [http://www.slac.stanford.edu/spires/find/hep/www?j=PHLTA,B125,487 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 [[asymptotic freedom|asymptotically free]]. However at low energies the theory becomes strongly coupled, and is better described by a [[Seiberg duality|Seiberg dual]] description in terms of [[Montonen–Olive duality|magnetic variables]] with the same global flavor symmetry group but a new gauge symmetry SU(M-N). Notice that the [[gauge symmetry|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.

==References==
* [https://arxiv.org/abs/hep-th/9509066 Lectures on supersymmetric gauge theories and electric-magnetic duality] by [[Nathan Seiberg]] and [[Kenneth Intriligator]].

{{Supersymmetry topics |state=collapsed}}
{{Quantum field theories}}

[[Category:Supersymmetric quantum field theory]]
[[Category:Quantum chromodynamics]]

Super QCD - Revision history

imported>OpenScience709: More precise category.