Black holes with baryonic charge and I $$ \mathcal{I} $$ -extremization
Abstract Recently it was discovered that twisted superconformal index I $$ \mathcal{I} $$ can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called I $$ \mathcal{I} $$ -extremization procedure to three-dimensio...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2019)050 |
| _version_ | 1818329202419564544 |
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| author | Hyojoong Kim Nakwoo Kim |
| author_facet | Hyojoong Kim Nakwoo Kim |
| author_sort | Hyojoong Kim |
| collection | DOAJ |
| description | Abstract Recently it was discovered that twisted superconformal index I $$ \mathcal{I} $$ can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called I $$ \mathcal{I} $$ -extremization procedure to three-dimensional gauge field theories and their geometric dual, focusing in particular on the seven-dimensional Sasaki-Einstein manifold M 1,1,1. We generalize recent studies on relations among toric geometry, variational principles, and black hole entropy to the case of AdS2 × Y 9, where Y 9 is a fibration of toric Sasaki-Einstein manifold M 1,1,1 over a two-dimensional Riemann surface Σ g . The nine-dimensional variational problem is given in terms of an entropy functional. In order to illustrate the computations as explicitly as possible, we consider cases where either only mesonic or baryonic fluxes are turned on. By employing the operator counting method, we calculate the S 3 free energy and the topologically twisted index I $$ \mathcal{I} $$ at large-N. The result for I $$ \mathcal{I} $$ , it turns out, can be also obtained from the variational principle of the entropy functional with mesonic fluxes. We also study asymptotically AdS4 black holes which are magnetically charged with respect to the vector field in the Betti multiplet. By extremizing the entropy functional with baryonic flux, we compute the entropy and find that it agrees with the entropy of an explicit solution in a four-dimensional gauged supergravity which is a consistent truncation of eleven-dimensional supergravity in AdS4 × M 1,1,1. |
| first_indexed | 2024-12-13T12:44:19Z |
| format | Article |
| id | doaj.art-a5a33a36d8954a039b02ec7419ed5cee |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T12:44:19Z |
| publishDate | 2019-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a5a33a36d8954a039b02ec7419ed5cee2022-12-21T23:45:33ZengSpringerOpenJournal of High Energy Physics1029-84792019-11-0120191112510.1007/JHEP11(2019)050Black holes with baryonic charge and I $$ \mathcal{I} $$ -extremizationHyojoong Kim0Nakwoo Kim1Department of Physics and Research Institute of Basic Science, Kyung Hee UniversityDepartment of Physics and Research Institute of Basic Science, Kyung Hee UniversityAbstract Recently it was discovered that twisted superconformal index I $$ \mathcal{I} $$ can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called I $$ \mathcal{I} $$ -extremization procedure to three-dimensional gauge field theories and their geometric dual, focusing in particular on the seven-dimensional Sasaki-Einstein manifold M 1,1,1. We generalize recent studies on relations among toric geometry, variational principles, and black hole entropy to the case of AdS2 × Y 9, where Y 9 is a fibration of toric Sasaki-Einstein manifold M 1,1,1 over a two-dimensional Riemann surface Σ g . The nine-dimensional variational problem is given in terms of an entropy functional. In order to illustrate the computations as explicitly as possible, we consider cases where either only mesonic or baryonic fluxes are turned on. By employing the operator counting method, we calculate the S 3 free energy and the topologically twisted index I $$ \mathcal{I} $$ at large-N. The result for I $$ \mathcal{I} $$ , it turns out, can be also obtained from the variational principle of the entropy functional with mesonic fluxes. We also study asymptotically AdS4 black holes which are magnetically charged with respect to the vector field in the Betti multiplet. By extremizing the entropy functional with baryonic flux, we compute the entropy and find that it agrees with the entropy of an explicit solution in a four-dimensional gauged supergravity which is a consistent truncation of eleven-dimensional supergravity in AdS4 × M 1,1,1.http://link.springer.com/article/10.1007/JHEP11(2019)050AdS-CFT CorrespondenceBlack Holes in String TheoryChern-Simons TheoriesField Theories in Lower Dimensions |
| spellingShingle | Hyojoong Kim Nakwoo Kim Black holes with baryonic charge and I $$ \mathcal{I} $$ -extremization Journal of High Energy Physics AdS-CFT Correspondence Black Holes in String Theory Chern-Simons Theories Field Theories in Lower Dimensions |
| title | Black holes with baryonic charge and I $$ \mathcal{I} $$ -extremization |
| title_full | Black holes with baryonic charge and I $$ \mathcal{I} $$ -extremization |
| title_fullStr | Black holes with baryonic charge and I $$ \mathcal{I} $$ -extremization |
| title_full_unstemmed | Black holes with baryonic charge and I $$ \mathcal{I} $$ -extremization |
| title_short | Black holes with baryonic charge and I $$ \mathcal{I} $$ -extremization |
| title_sort | black holes with baryonic charge and i mathcal i extremization |
| topic | AdS-CFT Correspondence Black Holes in String Theory Chern-Simons Theories Field Theories in Lower Dimensions |
| url | http://link.springer.com/article/10.1007/JHEP11(2019)050 |
| work_keys_str_mv | AT hyojoongkim blackholeswithbaryonicchargeandimathcaliextremization AT nakwookim blackholeswithbaryonicchargeandimathcaliextremization |