agree in any dual description. Evidence for Seiberg duality The moduli spaces of the dual theories are identical. The global symmetries agree, as do the charges of the mesons and baryons. In certain cases it reduces to ordinary electromagnetic duality. It may be embedded in string theory via Hanany–Witten brane cartoons consisting of intersecting D-branes. There it is realized as the motion of an NS5-brane which is conjectured to preserve the universality class. Six nontrivial anomalies may be computed on both sides of the duality, and they agree as they must in accordance with Gerard 't Hooft's anomaly matching conditions. The role of the additional fundamental meson superfield M in the dual theory is very crucial in matching the anomalies. The global gravitational anomalies also match up as the parity of the number of chiral fields is the same in both theories. The R-charge of the Weyl fermion in a chiral superfield is one less than the R-charge of the superfield. The R-charge of a gaugino is +1. Another evidence for Seiberg duality comes from identifying the superconformal index, which is a generalization of the Witten index, for the electric and the magnetic phase. The identification gives rise to complicated integral identities which have been studied in the mathematical literature. Generalizations 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. References Further reading Nathan Seiberg, Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories. David Tong, Supersymmetric Field Theory. Gauge theories Supersymmetric quantum field theory Quantum chromodynamics Duality theories Renormalization group