Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups

We compute the elliptic genera of two-dimensional N = (2, 2) and N = (0, 2)- gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is expressed as a sum over residues of a meromorphic function whose argument is the holonomy of the gauge field along both the spatial and the temporal directions of the torus. We illustrate our formulas by a few examples including the quintic Calabi?Yau, N =(2, 2) SU(2) and O(2) gauge theories coupled to N fundamental chiral multiplets, and a geometric N =(0, 2) model. © 2013 Springer Science+Business Media Dordrecht.