A geometric dual of c-extremization
We consider supersymmetric AdS3 × Y7 and AdS2 × Y9 solutions of type IIB and D = 11 supergravity, respectively, that are holographically dual to SCFTs with (0, 2) supersymmetry in two dimensions and N = 2 supersymmetry in one dimension. The geometry of Y2n+1, which can be defined for n ≥ 3, shares m...
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| Format: | Journal article |
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Springer Berlin Heidelberg
2019
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| _version_ | 1826275833747079168 |
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| author | Couzens, C Gauntlett, J Martelli, D Sparks, J |
| author_facet | Couzens, C Gauntlett, J Martelli, D Sparks, J |
| author_sort | Couzens, C |
| collection | OXFORD |
| description | We consider supersymmetric AdS3 × Y7 and AdS2 × Y9 solutions of type IIB and D = 11 supergravity, respectively, that are holographically dual to SCFTs with (0, 2) supersymmetry in two dimensions and N = 2 supersymmetry in one dimension. The geometry of Y2n+1, which can be defined for n ≥ 3, shares many similarities with SasakiEinstein geometry, including the existence of a canonical R-symmetry Killing vector, but there are also some crucial differences. We show that the R-symmetry Killing vector may be determined by extremizing a function that depends only on certain global, topological data. In particular, assuming it exists, for n = 3 one can compute the central charge of an AdS3 × Y7 solution without knowing its explicit form. We interpret this as a geometric dual of c-extremization in (0, 2) SCFTs. For the case of AdS2 × Y9 solutions we show that the extremal problem can be used to obtain properties of the dual quantum mechanics, including obtaining the entropy of a class of supersymmetric black holes in AdS4. We also study many specific examples of the type AdS3×T 2×Y5, including a new family of explicit supergravity solutions. In addition we discuss the possibility that the (0, 2) SCFTs dual to these solutions can arise from the compactification on T 2 of certain d = 4 quiver gauge theories associated with five-dimensional Sasaki-Einstein metrics and, surprisingly, come to a negative conclusion. |
| first_indexed | 2024-03-06T23:04:50Z |
| format | Journal article |
| id | oxford-uuid:636ae06e-02ee-45f7-82c9-84380bd14946 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:04:50Z |
| publishDate | 2019 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | oxford-uuid:636ae06e-02ee-45f7-82c9-84380bd149462022-03-26T18:12:49ZA geometric dual of c-extremizationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:636ae06e-02ee-45f7-82c9-84380bd14946Symplectic Elements at OxfordSpringer Berlin Heidelberg2019Couzens, CGauntlett, JMartelli, DSparks, JWe consider supersymmetric AdS3 × Y7 and AdS2 × Y9 solutions of type IIB and D = 11 supergravity, respectively, that are holographically dual to SCFTs with (0, 2) supersymmetry in two dimensions and N = 2 supersymmetry in one dimension. The geometry of Y2n+1, which can be defined for n ≥ 3, shares many similarities with SasakiEinstein geometry, including the existence of a canonical R-symmetry Killing vector, but there are also some crucial differences. We show that the R-symmetry Killing vector may be determined by extremizing a function that depends only on certain global, topological data. In particular, assuming it exists, for n = 3 one can compute the central charge of an AdS3 × Y7 solution without knowing its explicit form. We interpret this as a geometric dual of c-extremization in (0, 2) SCFTs. For the case of AdS2 × Y9 solutions we show that the extremal problem can be used to obtain properties of the dual quantum mechanics, including obtaining the entropy of a class of supersymmetric black holes in AdS4. We also study many specific examples of the type AdS3×T 2×Y5, including a new family of explicit supergravity solutions. In addition we discuss the possibility that the (0, 2) SCFTs dual to these solutions can arise from the compactification on T 2 of certain d = 4 quiver gauge theories associated with five-dimensional Sasaki-Einstein metrics and, surprisingly, come to a negative conclusion. |
| spellingShingle | Couzens, C Gauntlett, J Martelli, D Sparks, J A geometric dual of c-extremization |
| title | A geometric dual of c-extremization |
| title_full | A geometric dual of c-extremization |
| title_fullStr | A geometric dual of c-extremization |
| title_full_unstemmed | A geometric dual of c-extremization |
| title_short | A geometric dual of c-extremization |
| title_sort | geometric dual of c extremization |
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