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| Main Authors: | , |
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| Format: | Preprint |
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2021
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| Online Access: | https://arxiv.org/abs/2110.01538 |
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| _version_ | 1866915067349434368 |
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| author | Ardehali, Arash Arabi Hong, Junho |
| author_facet | Ardehali, Arash Arabi Hong, Junho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_01538 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions Ardehali, Arash Arabi Hong, Junho High Energy Physics - Theory Mathematical Physics 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. |
| title | Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2110.01538 |