The asymptotic growth of states of the 4d N = 1 $$ \mathcal{N}=1 $$ superconformal index
Abstract We show that the superconformal index of N = 1 $$ \mathcal{N}=1 $$ superconformal field theories in four dimensions has an asymptotic growth of states which is exponential in the charges. Our analysis holds in a Cardy-like limit of large charges, for which the index is dominated by small va...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP08(2019)120 |
| _version_ | 1818281632506839040 |
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| author | Alejandro Cabo-Bizet Davide Cassani Dario Martelli Sameer Murthy |
| author_facet | Alejandro Cabo-Bizet Davide Cassani Dario Martelli Sameer Murthy |
| author_sort | Alejandro Cabo-Bizet |
| collection | DOAJ |
| description | Abstract We show that the superconformal index of N = 1 $$ \mathcal{N}=1 $$ superconformal field theories in four dimensions has an asymptotic growth of states which is exponential in the charges. Our analysis holds in a Cardy-like limit of large charges, for which the index is dominated by small values of chemical potentials. In this limit we find the saddle points of the integral that defines the superconformal index using two different methods. One method, valid for finite N, is to first take the Cardy-like limit and then find the saddle points. The other method is to analyze the saddle points at large N and then take the Cardy-like limit. The result of both analyses is that the asymptotic growth of states of the superconformal index exactly agrees with the Bekenstein-Hawking entropy of supersymmetric black holes in the dual AdS5 theory. |
| first_indexed | 2024-12-13T00:08:12Z |
| format | Article |
| id | doaj.art-85006af87b8c45d38429525dbbe3ff05 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T00:08:12Z |
| publishDate | 2019-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-85006af87b8c45d38429525dbbe3ff052022-12-22T00:06:08ZengSpringerOpenJournal of High Energy Physics1029-84792019-08-012019813310.1007/JHEP08(2019)120The asymptotic growth of states of the 4d N = 1 $$ \mathcal{N}=1 $$ superconformal indexAlejandro Cabo-Bizet0Davide Cassani1Dario Martelli2Sameer Murthy3Department of Mathematics, King’s College LondonINFN, Sezione di PadovaDepartment of Mathematics, King’s College LondonDepartment of Mathematics, King’s College LondonAbstract We show that the superconformal index of N = 1 $$ \mathcal{N}=1 $$ superconformal field theories in four dimensions has an asymptotic growth of states which is exponential in the charges. Our analysis holds in a Cardy-like limit of large charges, for which the index is dominated by small values of chemical potentials. In this limit we find the saddle points of the integral that defines the superconformal index using two different methods. One method, valid for finite N, is to first take the Cardy-like limit and then find the saddle points. The other method is to analyze the saddle points at large N and then take the Cardy-like limit. The result of both analyses is that the asymptotic growth of states of the superconformal index exactly agrees with the Bekenstein-Hawking entropy of supersymmetric black holes in the dual AdS5 theory.http://link.springer.com/article/10.1007/JHEP08(2019)120AdS-CFT CorrespondenceBlack Holes in String TheorySupersymmetric Gauge TheoryConformal Field Theory |
| spellingShingle | Alejandro Cabo-Bizet Davide Cassani Dario Martelli Sameer Murthy The asymptotic growth of states of the 4d N = 1 $$ \mathcal{N}=1 $$ superconformal index Journal of High Energy Physics AdS-CFT Correspondence Black Holes in String Theory Supersymmetric Gauge Theory Conformal Field Theory |
| title | The asymptotic growth of states of the 4d N = 1 $$ \mathcal{N}=1 $$ superconformal index |
| title_full | The asymptotic growth of states of the 4d N = 1 $$ \mathcal{N}=1 $$ superconformal index |
| title_fullStr | The asymptotic growth of states of the 4d N = 1 $$ \mathcal{N}=1 $$ superconformal index |
| title_full_unstemmed | The asymptotic growth of states of the 4d N = 1 $$ \mathcal{N}=1 $$ superconformal index |
| title_short | The asymptotic growth of states of the 4d N = 1 $$ \mathcal{N}=1 $$ superconformal index |
| title_sort | asymptotic growth of states of the 4d n 1 mathcal n 1 superconformal index |
| topic | AdS-CFT Correspondence Black Holes in String Theory Supersymmetric Gauge Theory Conformal Field Theory |
| url | http://link.springer.com/article/10.1007/JHEP08(2019)120 |
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