Supersymmetric partition functions on Riemann surfaces

By F. Benini, Alberto Zaffaroni. 2016

211 citations recorded by the source corpus.

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

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/597f0604e8b5f9a1b2de1ce2a049af18ccf358ae

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In Nuclear and High Energy Physics

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Citations in the corpus

Exact microstate counting for dyonic black holes in AdS4 (2016, methodology): “The large N expression for the index of ABJM was found in [3, 21] for the case of real ua , and we can extend it to the complex plane using holomorphy:”
Comments on twisted indices in 3d supersymmetric gauge theories (2016, background): “a of [38]. It would be very interesting to study this correspondence further. Note added: During the nal stage of writing, we became aware of another closely related work by F. Benini and A. Zaaroni [41]. We are grateful to them for giving us a few more days to nish writing our paper, and for coordi”
Black Holes in 4D N=4 Super-Yang-Mills Field Theory (2018, background): “There, the Bekenstein-Hawking entropy of a class of static dyonic BPS black holes in AdS4 was holographically reproduced in the dual CFT3, via supersymmetric localization [12–14].”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, methodology): “They can be derived by supersymmetric localization, similarly to the three-dimensional case studied in [27]—see also [22, 23, 17, 19, 20, 27].”