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arXiv · 1711.05669

Analytic continuation of dimensions in supersymmetric localization

Anastasios Gorantis·Joseph A. Minahan·Usman Naseer
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Abstract

We compute the perturbative partition functions for gauge theories with eight supersymmetries on spheres of dimension $d\le5$, proving a conjecture by the second author. We apply similar methods to gauge theories with four supersymmetries on spheres with $d\le3$. The results are valid for non-integer $d$ as well. We further propose an analytic continuation from $d=3$ to $d=4$ that gives the perturbative partition function for an $\mathcal{N}=1$ gauge theory. The results are consistent with the free multiplets and the one-loop $β$-functions for general $\mathcal{N}=1$ gauge theories. We also consider the analytic continuation of an $\mathcal{N}=1$-preserving mass deformation of the maximally supersymmetric gauge theory and compare to recent holographic results for $\mathcal{N}=1^*$ super Yang-Mills. We find that the general structure for the real part of the free energy coming from the analytic continuation is consistent with the holographic results.

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Anastasios Gorantis, Joseph A. Minahan, Usman Naseer. 2018-02-21. Analytic continuation of dimensions in supersymmetric localization. https://doi.org/10.1007/jhep02(2018)070

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