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, whereΣg 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.
Benini, F., Zaffaroni, A. (2017). Supersymmetric partition functions on Riemann surfaces. Intervento presentato a: proceedings of the conference String-Math, 2015, chn [10.1090/pspum/096/01654].
Supersymmetric partition functions on Riemann surfaces
Zaffaroni, A
2017
Abstract
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, whereΣg 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.
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