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 $Sigma_g imes T^n$ 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. We also show that the large N partition function of ABJM theory on $Sigma_g imes S^1$ reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS$_4$ whose horizon has $Sigma_g$ topology.

Supersymmetric partition functions on Riemann surfaces / Benini, Francesco; Zaffaroni, Alberto. - 96(2017), pp. 13-46. ((Intervento presentato al convegno Conference String-Math 2015 tenutosi a Tsinghua Sanya International Mathematics Forum in Sanya, China nel December 31, 2015–January 4, 2016 [10.1090/pspum/096/01654].

Supersymmetric partition functions on Riemann surfaces

Benini, Francesco;
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 $Sigma_g imes T^n$ 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. We also show that the large N partition function of ABJM theory on $Sigma_g imes S^1$ reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS$_4$ whose horizon has $Sigma_g$ topology.
String-Math 2015
PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS
96
13
46
9781470442767
978-1-4704-2951-5
http://arxiv.org/abs/1605.06120v2
American Mathematical Society & International Press of Boston
Benini, Francesco; Zaffaroni, Alberto
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/60608
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