Elliptic Genera of 2d N=2 Gauge Theories

We compute the elliptic genera of general two-dimensional and gauge theories. We find that the elliptic genus is given by the sum of Jeffrey-Kirwan residues of a meromorphic form, representing the one-loop determinant of fields, on the moduli space of flat connections on T (2). We give several examples illustrating our formula, with both Abelian and non-Abelian gauge groups, and discuss some dualities for U(k) and SU(k) theories. This paper is a sequel to the authors' previous paper (Benini et al., Lett Math Phys 104:465-493, 2014).