2016/05/31 by Francesco Benini, Alberto Zaffaroni · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.AG #math.MP
paper · pdf · doi:10.1090/pspum/096
published as Proc.Symp.Pure Math. 96 (2017) 13-46 · 34 pages, 1 figure
arxiv created 2017/09/01 · arxiv updated 2018/05/18
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 Σg × Tn with partial topological twist on Σg, where Σg is a Riemann surface of arbitrary genus and Tn 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 S1. 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. We also show that the large N partition function of ABJM theory on Σg × S1 reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS4 whose horizon has Σg topology.