Equivariant localization for AdS/CFT
Abstract We explain how equivariant localization may be applied to AdS/CFT to compute various BPS observables in gravity, such as central charges and conformal dimensions of chiral primary operators, without solving the supergravity equations. The key ingredient is that supersymmetric AdS solutions...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2024)015 |
| _version_ | 1797276126198890496 |
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| author | Pietro Benetti Genolini Jerome P. Gauntlett James Sparks |
| author_facet | Pietro Benetti Genolini Jerome P. Gauntlett James Sparks |
| author_sort | Pietro Benetti Genolini |
| collection | DOAJ |
| description | Abstract We explain how equivariant localization may be applied to AdS/CFT to compute various BPS observables in gravity, such as central charges and conformal dimensions of chiral primary operators, without solving the supergravity equations. The key ingredient is that supersymmetric AdS solutions with an R-symmetry are equipped with a set of equivariantly closed forms. These may in turn be used to impose flux quantization and compute observables for supergravity solutions, using only topological information and the Berline-Vergne-Atiyah-Bott fixed point formula. We illustrate the formalism by considering AdS 5 × M 6 and AdS 3 × M 8 solutions of D = 11 supergravity. As well as recovering results for many classes of well-known supergravity solutions, without using any knowledge of their explicit form, we also compute central charges for which explicit supergravity solutions have not been constructed. |
| first_indexed | 2024-03-07T15:23:51Z |
| format | Article |
| id | doaj.art-62033d07984f4b9ea322c64eebe85189 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-07T15:23:51Z |
| publishDate | 2024-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-62033d07984f4b9ea322c64eebe851892024-03-05T17:27:34ZengSpringerOpenJournal of High Energy Physics1029-84792024-02-012024215310.1007/JHEP02(2024)015Equivariant localization for AdS/CFTPietro Benetti Genolini0Jerome P. Gauntlett1James Sparks2Department of Mathematics, King’s College LondonBlackett Laboratory, Imperial CollegeMathematical Institute, University of OxfordAbstract We explain how equivariant localization may be applied to AdS/CFT to compute various BPS observables in gravity, such as central charges and conformal dimensions of chiral primary operators, without solving the supergravity equations. The key ingredient is that supersymmetric AdS solutions with an R-symmetry are equipped with a set of equivariantly closed forms. These may in turn be used to impose flux quantization and compute observables for supergravity solutions, using only topological information and the Berline-Vergne-Atiyah-Bott fixed point formula. We illustrate the formalism by considering AdS 5 × M 6 and AdS 3 × M 8 solutions of D = 11 supergravity. As well as recovering results for many classes of well-known supergravity solutions, without using any knowledge of their explicit form, we also compute central charges for which explicit supergravity solutions have not been constructed.https://doi.org/10.1007/JHEP02(2024)015AdS-CFT CorrespondenceSupergravity ModelsD-Branes |
| spellingShingle | Pietro Benetti Genolini Jerome P. Gauntlett James Sparks Equivariant localization for AdS/CFT Journal of High Energy Physics AdS-CFT Correspondence Supergravity Models D-Branes |
| title | Equivariant localization for AdS/CFT |
| title_full | Equivariant localization for AdS/CFT |
| title_fullStr | Equivariant localization for AdS/CFT |
| title_full_unstemmed | Equivariant localization for AdS/CFT |
| title_short | Equivariant localization for AdS/CFT |
| title_sort | equivariant localization for ads cft |
| topic | AdS-CFT Correspondence Supergravity Models D-Branes |
| url | https://doi.org/10.1007/JHEP02(2024)015 |
| work_keys_str_mv | AT pietrobenettigenolini equivariantlocalizationforadscft AT jeromepgauntlett equivariantlocalizationforadscft AT jamessparks equivariantlocalizationforadscft |