A CFT distance conjecture
Abstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metr...
| Main Authors: | , , , |
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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 |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP10(2021)070 |
| _version_ | 1819109146076643328 |
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| author | Eric Perlmutter Leonardo Rastelli Cumrun Vafa Irene Valenzuela |
| author_facet | Eric Perlmutter Leonardo Rastelli Cumrun Vafa Irene Valenzuela |
| author_sort | Eric Perlmutter |
| collection | DOAJ |
| description | Abstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions. |
| first_indexed | 2024-12-22T03:21:11Z |
| format | Article |
| id | doaj.art-914f676bd1b945bcb65377731db9c995 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T03:21:11Z |
| publishDate | 2021-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-914f676bd1b945bcb65377731db9c9952022-12-21T18:40:44ZengSpringerOpenJournal of High Energy Physics1029-84792021-10-0120211013310.1007/JHEP10(2021)070A CFT distance conjectureEric Perlmutter0Leonardo Rastelli1Cumrun Vafa2Irene Valenzuela3Walter Burke Institute for Theoretical Physics, CaltechYang Institute for Theoretical Physics, Stony Brook UniversityJefferson Physical Laboratory, Harvard UniversityJefferson Physical Laboratory, Harvard UniversityAbstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.https://doi.org/10.1007/JHEP10(2021)070AdS-CFT CorrespondenceConformal Field Theory |
| spellingShingle | Eric Perlmutter Leonardo Rastelli Cumrun Vafa Irene Valenzuela A CFT distance conjecture Journal of High Energy Physics AdS-CFT Correspondence Conformal Field Theory |
| title | A CFT distance conjecture |
| title_full | A CFT distance conjecture |
| title_fullStr | A CFT distance conjecture |
| title_full_unstemmed | A CFT distance conjecture |
| title_short | A CFT distance conjecture |
| title_sort | cft distance conjecture |
| topic | AdS-CFT Correspondence Conformal Field Theory |
| url | https://doi.org/10.1007/JHEP10(2021)070 |
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