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Renormalization group duality in supersymmetric gauge theories

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.

Being an S duality, Seiberg duality relates the strong coupling regime with the weak coupling regime, and interchanges chromoelectric fields (gluons) with chromomagnetic fields (gluons of the dual gauge group), and chromoelectric charges (quarks) with nonabelian 't Hooft–Polyakov monopoles. In particular, the Higgs phase is dual to the confinement phase as in the dual superconducting model. The mesons and baryons are preserved by the duality. However, in the electric theory the meson is a quark bilinear , while in the magnetic theory it is a fundamental field. In both theories the baryons are constructed from quarks, but the number of quarks in one baryon is the rank of the gauge group, which differs in the two dual theories. The gauge symmetries of the theories do not agree, which is not problematic as the gauge symmetry is a feature of the formulation and not of the fundamental physics. The global symmetries relate distinct physical configurations, and so they need to agree in any dual description.

Seiberg duality has been generalized in many directions. One generalization applies to quiver gauge theories, in which the flavor symmetries are also gauged. The simplest of these is a super QCD with the flavor group gauged and an additional term in the superpotential. It leads to a series of Seiberg dualities known as a duality cascade, introduced by Igor Klebanov and Matthew Strassler. Whether Seiberg duality exists in 3 dimensional nonabelian gauge theories with only 4 supercharges is not known, although it is conjectured in some special cases with Chern–Simons terms.