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2016

Supersymmetric partition functions on Riemann surfaces

Benini, Francesco, Zaffaroni, Alberto

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We present a compact formula for the supersymmetric partition function of 2d N=(2,2), 3d N=2 and 4d N=1 gauge theories on $\Sigma_g \times T^n$ with partial topological twist on $\Sigma_g$, where $\Sigma_g$ is a Riemann surface of arbitrary genus and $T^n$ is a torus with n=0,1,2, respectively.

In 2d we also include certain local operator insertions, and in 3d we include Wilson line operator insertions along $S^1$.
For genus g=1, the formula computes the Witten index.
We present a few simple Abelian and non-Abelian examples, including new tests of non-perturbative dualities.