SL(3, ℤ) Modularity and New Cardy limits of the N $$ \mathcal{N} $$ = 4 superconformal index
Abstract The entropy of 1/16-th BPS AdS5 black holes can be microscopically accounted for by the superconformal index of the N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory. One way to compute this is through a Cardy-like limit of a formula for the index obtained in [1] using the “S-transformation”...
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oai:doaj.org-article:b61f4c7c15294e9a82565a3f6cda2dc12021-11-14T12:41:13ZSL(3, ℤ) Modularity and New Cardy limits of the N $$ \mathcal{N} $$ = 4 superconformal index10.1007/JHEP11(2021)0471029-8479https://doaj.org/article/b61f4c7c15294e9a82565a3f6cda2dc12021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)047https://doaj.org/toc/1029-8479Abstract The entropy of 1/16-th BPS AdS5 black holes can be microscopically accounted for by the superconformal index of the N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory. One way to compute this is through a Cardy-like limit of a formula for the index obtained in [1] using the “S-transformation” of the elliptic Γ function. In this paper, we derive more general SL(3, ℤ) modular properties of the elliptic Γ function. We then use these properties to obtain a three integer parameter family of generalized Cardy-like limits of the N $$ \mathcal{N} $$ = 4 superconformal index. From these limits, we obtain entropy formulae that have a similar form as that of the original AdS5 black hole, up to an overall rescaling of the entropy. We interpret this both on the field theory and the gravitational side. Finally, we comment on how our work suggests a generalization of the Farey tail to four dimensions.Vishnu JejjalaYang LeiSam van LeuvenWei LiSpringerOpenarticleAdS-CFT CorrespondenceSupersymmetric Gauge TheoryBlack Holes in String TheoryNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-77 (2021) |
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DOAJ |
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DOAJ |
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EN |
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AdS-CFT Correspondence Supersymmetric Gauge Theory Black Holes in String Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 |
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AdS-CFT Correspondence Supersymmetric Gauge Theory Black Holes in String Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Vishnu Jejjala Yang Lei Sam van Leuven Wei Li SL(3, ℤ) Modularity and New Cardy limits of the N $$ \mathcal{N} $$ = 4 superconformal index |
| description |
Abstract The entropy of 1/16-th BPS AdS5 black holes can be microscopically accounted for by the superconformal index of the N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory. One way to compute this is through a Cardy-like limit of a formula for the index obtained in [1] using the “S-transformation” of the elliptic Γ function. In this paper, we derive more general SL(3, ℤ) modular properties of the elliptic Γ function. We then use these properties to obtain a three integer parameter family of generalized Cardy-like limits of the N $$ \mathcal{N} $$ = 4 superconformal index. From these limits, we obtain entropy formulae that have a similar form as that of the original AdS5 black hole, up to an overall rescaling of the entropy. We interpret this both on the field theory and the gravitational side. Finally, we comment on how our work suggests a generalization of the Farey tail to four dimensions. |
| format |
article |
| author |
Vishnu Jejjala Yang Lei Sam van Leuven Wei Li |
| author_facet |
Vishnu Jejjala Yang Lei Sam van Leuven Wei Li |
| author_sort |
Vishnu Jejjala |
| title |
SL(3, ℤ) Modularity and New Cardy limits of the N $$ \mathcal{N} $$ = 4 superconformal index |
| title_short |
SL(3, ℤ) Modularity and New Cardy limits of the N $$ \mathcal{N} $$ = 4 superconformal index |
| title_full |
SL(3, ℤ) Modularity and New Cardy limits of the N $$ \mathcal{N} $$ = 4 superconformal index |
| title_fullStr |
SL(3, ℤ) Modularity and New Cardy limits of the N $$ \mathcal{N} $$ = 4 superconformal index |
| title_full_unstemmed |
SL(3, ℤ) Modularity and New Cardy limits of the N $$ \mathcal{N} $$ = 4 superconformal index |
| title_sort |
sl(3, ℤ) modularity and new cardy limits of the n $$ \mathcal{n} $$ = 4 superconformal index |
| publisher |
SpringerOpen |
| publishDate |
2021 |
| url |
https://doaj.org/article/b61f4c7c15294e9a82565a3f6cda2dc1 |
| work_keys_str_mv |
AT vishnujejjala sl3zmodularityandnewcardylimitsofthenmathcaln4superconformalindex AT yanglei sl3zmodularityandnewcardylimitsofthenmathcaln4superconformalindex AT samvanleuven sl3zmodularityandnewcardylimitsofthenmathcaln4superconformalindex AT weili sl3zmodularityandnewcardylimitsofthenmathcaln4superconformalindex |
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