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In this paper we describe a systematic method to compute elliptic genera of(2,2) supersymmetric gauge theories in two dimensions with gauge group G/Gamma(for G semisimple and simply-connected, Gamma a subgroup of the center of G)with various discrete theta angles. We apply the technique to examples of puregauge theories with low-rank gauge groups. Our results are consistent withexpectations from decomposition of two-dimensional theories with finite globalone-form symmetries and with computations of supersymmetry breaking for somediscrete theta angles in pure gauge theories. Finally, we make predictions forthe elliptic genera of all the other remaining pure gauge theories by applyingdecomposition and matching to known supersymmetry breaking patterns.

Elliptic genera of pure gauge theories in two dimensions with semisimple non-simply-connected gauge groups