The topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail
Abstract We investigate the large-N asymptotics of the topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills (SYM) theory on T 2 × S 2 and provide its holographic interpretation based on the black hole Farey tail [1]. In the field theory side, we use the Bethe-Ansatz (BA) for...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP10(2021)145 |
| _version_ | 1818966799226503168 |
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| author | Junho Hong |
| author_facet | Junho Hong |
| author_sort | Junho Hong |
| collection | DOAJ |
| description | Abstract We investigate the large-N asymptotics of the topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills (SYM) theory on T 2 × S 2 and provide its holographic interpretation based on the black hole Farey tail [1]. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of N $$ \mathcal{N} $$ = 4 SYM theory as a discrete sum over Bethe vacua, to compute the large-N asymptotics of the twisted index. In a dual N $$ \mathcal{N} $$ = 2 gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-N limit. This extends the previous microstate counting of an AdS5 black string by the twisted index and thereby improves holographic understanding of the twisted index. |
| first_indexed | 2024-12-20T13:38:38Z |
| format | Article |
| id | doaj.art-0afd9741c5234d2d964a51bde6e82f5e |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T13:38:38Z |
| publishDate | 2021-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-0afd9741c5234d2d964a51bde6e82f5e2022-12-21T19:38:52ZengSpringerOpenJournal of High Energy Physics1029-84792021-10-0120211014910.1007/JHEP10(2021)145The topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tailJunho Hong0Leinweber Center for Theoretical Physics, Randall Laboratory of Physics, The University of MichiganAbstract We investigate the large-N asymptotics of the topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills (SYM) theory on T 2 × S 2 and provide its holographic interpretation based on the black hole Farey tail [1]. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of N $$ \mathcal{N} $$ = 4 SYM theory as a discrete sum over Bethe vacua, to compute the large-N asymptotics of the twisted index. In a dual N $$ \mathcal{N} $$ = 2 gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-N limit. This extends the previous microstate counting of an AdS5 black string by the twisted index and thereby improves holographic understanding of the twisted index.https://doi.org/10.1007/JHEP10(2021)145AdS-CFT CorrespondenceBlack Holes in String TheorySupersymmetric Gauge Theory |
| spellingShingle | Junho Hong The topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail Journal of High Energy Physics AdS-CFT Correspondence Black Holes in String Theory Supersymmetric Gauge Theory |
| title | The topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail |
| title_full | The topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail |
| title_fullStr | The topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail |
| title_full_unstemmed | The topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail |
| title_short | The topologically twisted index of N $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail |
| title_sort | topologically twisted index of n mathcal n 4 su n super yang mills theory and a black hole farey tail |
| topic | AdS-CFT Correspondence Black Holes in String Theory Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP10(2021)145 |
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