Resurgence, conformal blocks, and the sum over geometries in quantum gravity

Journal Article · Fri May 19 00:00:00 EDT 2023 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep05(2023)166· OSTI ID:2223068

Benjamin, Nathan ^[1]; Collier, Scott ^[2]; Maloney, Alexander ^[3]; Meruliya, Viraj ^[3]

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1. California Institute of Technology (CalTech), Pasadena, CA (United States); California Institute of Technology
2. Princeton University, NJ (United States)
3. McGill University, Montreal, QC (Canada)

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.

• Research Organization: California Institute of Technology (CalTech), Pasadena, CA (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0011632
• OSTI ID: 2223068
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 5 Vol. 2023; ISSN 1029-8479
• Publisher: Springer Nature
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AdS-CFT Correspondence
Conformal and W Symmetry
Field Theories in Lower Dimensions
Nonperturbative Effects