Index calculation by means of harmonic expansion

Abstract

We review derivation of superconformal indices by means of supersymmetric localization and spherical harmonic expansion for 3d N = 2, 4d N = 1, and 6d N = (1, 0) supersymmetric gauge theories. We demonstrate calculation of indices for vector multiplets in each dimension by analyzing energy eigenmodes in Sp × ℝ. For the 6d index we consider the perturbative contribution only. We focus on the technical details of harmonic expansion rather than physical applications.