Vanishing superconformal indices and the chiral symmetry breaking

Abstract

Superconformal indices of 4d N = 1 SYM theories with SU(N) and SP(2N) gauge groups are investigated for N f = N and N f = N + 1 flavors, respectively. These indices vanish for generic values of the flavor fugacities. However, for a singular submanifold of fugacities they behave like the Dirac delta functions and describe the chiral symmetry breaking phenomenon. Similar picture holds for partition functions of 3d supersymmetric field theories with the chiral symmetry breaking. © 2014 The Author(s).