Resurgence, conformal blocks, and the sum over geometries in quantum gravity
Abstract In two dimensional conformal field theories the limit of large central charge plays the role of a semi-classical limit. Certain universal observables, such as conformal blocks involving the exchange of the identity operator, can be expanded around this classical limit in powers of the centr...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2023)166 |
| _version_ | 1797736469036531712 |
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| author | Nathan Benjamin Scott Collier Alexander Maloney Viraj Meruliya |
| author_facet | Nathan Benjamin Scott Collier Alexander Maloney Viraj Meruliya |
| author_sort | Nathan Benjamin |
| collection | DOAJ |
| description | Abstract In two dimensional conformal field theories the limit of large central charge plays the role of a semi-classical limit. Certain universal observables, such as conformal blocks involving the exchange of the identity operator, can be expanded around this classical limit in powers of the central charge c. This expansion is an asymptotic series, so — via the same resurgence analysis familiar from quantum mechanics — necessitates the existence of non-perturbative effects. In the case of identity conformal blocks, these new effects have a simple interpretation: the CFT must possess new primary operators with dimension of order the central charge. This constrains the data of CFTs with large central charge in a way that is similar to (but distinct from) the conformal bootstrap. We study this phenomenon in three ways: numerically, analytically using Zamolodchikov’s recursion relations, and by considering non-unitary minimal models with large (negative) central charge. In the holographic dual to a CFT2, the expansion in powers of c is the perturbative loop expansion in powers of ћ. So our results imply that the graviton loop expansion is an asymptotic series, whose cure requires the inclusion of new saddle points in the gravitational path integral. In certain cases these saddle points have a simple interpretation: they are conical excesses, particle-like states with negative mass which are not in the physical spectrum but nevertheless appear as non-manifold saddle points that control the asymptotic behaviour of the loop expansion. This phenomenon also has an interpretation in SL(2, ℝ) Chern-Simons theory, where the non-perturbative effects are associated with the non-Teichmüller component of the moduli space of flat connections. |
| first_indexed | 2024-03-12T13:13:11Z |
| format | Article |
| id | doaj.art-30e894dbdac14149b5ff64b3d08d43cb |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T13:13:11Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-30e894dbdac14149b5ff64b3d08d43cb2023-08-27T11:06:18ZengSpringerOpenJournal of High Energy Physics1029-84792023-05-012023513910.1007/JHEP05(2023)166Resurgence, conformal blocks, and the sum over geometries in quantum gravityNathan Benjamin0Scott Collier1Alexander Maloney2Viraj Meruliya3Walter Burke Institute for Theoretical Physics, CaltechPrinceton Center for Theoretical Science, Princeton UniversityDepartment of Physics, McGill UniversityDepartment of Physics, McGill UniversityAbstract In two dimensional conformal field theories the limit of large central charge plays the role of a semi-classical limit. Certain universal observables, such as conformal blocks involving the exchange of the identity operator, can be expanded around this classical limit in powers of the central charge c. This expansion is an asymptotic series, so — via the same resurgence analysis familiar from quantum mechanics — necessitates the existence of non-perturbative effects. In the case of identity conformal blocks, these new effects have a simple interpretation: the CFT must possess new primary operators with dimension of order the central charge. This constrains the data of CFTs with large central charge in a way that is similar to (but distinct from) the conformal bootstrap. We study this phenomenon in three ways: numerically, analytically using Zamolodchikov’s recursion relations, and by considering non-unitary minimal models with large (negative) central charge. In the holographic dual to a CFT2, the expansion in powers of c is the perturbative loop expansion in powers of ћ. So our results imply that the graviton loop expansion is an asymptotic series, whose cure requires the inclusion of new saddle points in the gravitational path integral. In certain cases these saddle points have a simple interpretation: they are conical excesses, particle-like states with negative mass which are not in the physical spectrum but nevertheless appear as non-manifold saddle points that control the asymptotic behaviour of the loop expansion. This phenomenon also has an interpretation in SL(2, ℝ) Chern-Simons theory, where the non-perturbative effects are associated with the non-Teichmüller component of the moduli space of flat connections.https://doi.org/10.1007/JHEP05(2023)166AdS-CFT CorrespondenceConformal and W SymmetryField Theories in Lower DimensionsNonperturbative Effects |
| spellingShingle | Nathan Benjamin Scott Collier Alexander Maloney Viraj Meruliya Resurgence, conformal blocks, and the sum over geometries in quantum gravity Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry Field Theories in Lower Dimensions Nonperturbative Effects |
| title | Resurgence, conformal blocks, and the sum over geometries in quantum gravity |
| title_full | Resurgence, conformal blocks, and the sum over geometries in quantum gravity |
| title_fullStr | Resurgence, conformal blocks, and the sum over geometries in quantum gravity |
| title_full_unstemmed | Resurgence, conformal blocks, and the sum over geometries in quantum gravity |
| title_short | Resurgence, conformal blocks, and the sum over geometries in quantum gravity |
| title_sort | resurgence conformal blocks and the sum over geometries in quantum gravity |
| topic | AdS-CFT Correspondence Conformal and W Symmetry Field Theories in Lower Dimensions Nonperturbative Effects |
| url | https://doi.org/10.1007/JHEP05(2023)166 |
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