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arXiv · 2110.01538

Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions

Arash Arabi Ardehali·Junho Hong
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Abstract

We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories. Localization allows expressing such partition functions as an integral over a BPS moduli space. When the limit of interest introduces a scale hierarchy in the problem, asymptotics of the partition function is obtained in the Wilsonian approach by $i)$ decomposing (in some suitable scheme) the BPS moduli space into various patches according to the set of light fields (lighter than the scheme dependent cut-off $Λ$) they support, $ii)$ localizing the partition function of the effective field theory on each patch (with cut-offs set by the scheme), and $iii)$ summing up the contributions of all patches to obtain the final asymptotic result (which is scheme-independent and accurate as $Λ\to\infty$). Our prototype concerns the Cardy-like asymptotics of the 4d superconformal index, which has been of interest recently for its application to black hole microstate counting in AdS$_5$/CFT$_4$. As a byproduct of our analysis we obtain the most general asymptotic expression for the index of gauge theories in the Cardy-like limit, encompassing and extending all previous results.

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Arash Arabi Ardehali, Junho Hong. 2024-12-17. Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions. https://doi.org/10.1007/jhep01(2022)062

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