Elliptic Genera of Two-Dimensional N=2 Gauge Theories with Rank-One Gauge Groups

We compute the elliptic genera of two-dimensional and -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, SU(2) and O(2) gauge theories coupled to N fundamental chiral multiplets, and a geometric model.