Resurgence in Liouville theory
Liouville conformal field theory is a prototypical example of an exactly solvable quantum field theory, in the sense that the correlation functions in an arbitrary background can be determined exactly using only the constraints of unitarity and crossing symmetry. For example, the three point correla...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2025
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| Online Access: | https://hdl.handle.net/1721.1/157950 |
| _version_ | 1824458373806948352 |
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| author | Benjamin, Nathan Collier, Scott Maloney, Alexander Meruliya, Viraj |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Benjamin, Nathan Collier, Scott Maloney, Alexander Meruliya, Viraj |
| author_sort | Benjamin, Nathan |
| collection | MIT |
| description | Liouville conformal field theory is a prototypical example of an exactly solvable quantum field theory, in the sense that the correlation functions in an arbitrary background can be determined exactly using only the constraints of unitarity and crossing symmetry. For example, the three point correlation functions are given by the famous formula of Dorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ). Unlike many other exactly solvable theories, Liouville theory has a continuously tunable parameter — essentially ℏ — which is related to the central charge of the theory. Here we investigate the nature of the perturbative expansion in powers of ℏ, which is the loop expansion around a semi-classical solution. We show that the perturbative coefficients grow factorially, as expected of a Feynman diagram expansion, and take the form of an asymptotic series. We identify the singularities in the Borel plane, and show that they are associated with complex instanton solutions of Liouville theory; they correspond precisely to the complex solutions described by Harlow, Maltz, and Witten. Both single- and multi-valued solutions of Liouville appear. We show that the perturbative loop expansions around these different saddle points mix in the way expected for a trans-series expansion. Thus Liouville theory provides a calculable example of a quantum field theory where perturbative and instanton contributions can be summed up and assembled into a finite answer. |
| first_indexed | 2025-02-19T04:24:52Z |
| format | Article |
| id | mit-1721.1/157950 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2025-02-19T04:24:52Z |
| publishDate | 2025 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1579502025-01-09T03:10:15Z Resurgence in Liouville theory Benjamin, Nathan Collier, Scott Maloney, Alexander Meruliya, Viraj Massachusetts Institute of Technology. Center for Theoretical Physics Liouville conformal field theory is a prototypical example of an exactly solvable quantum field theory, in the sense that the correlation functions in an arbitrary background can be determined exactly using only the constraints of unitarity and crossing symmetry. For example, the three point correlation functions are given by the famous formula of Dorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ). Unlike many other exactly solvable theories, Liouville theory has a continuously tunable parameter — essentially ℏ — which is related to the central charge of the theory. Here we investigate the nature of the perturbative expansion in powers of ℏ, which is the loop expansion around a semi-classical solution. We show that the perturbative coefficients grow factorially, as expected of a Feynman diagram expansion, and take the form of an asymptotic series. We identify the singularities in the Borel plane, and show that they are associated with complex instanton solutions of Liouville theory; they correspond precisely to the complex solutions described by Harlow, Maltz, and Witten. Both single- and multi-valued solutions of Liouville appear. We show that the perturbative loop expansions around these different saddle points mix in the way expected for a trans-series expansion. Thus Liouville theory provides a calculable example of a quantum field theory where perturbative and instanton contributions can be summed up and assembled into a finite answer. 2025-01-08T19:47:24Z 2025-01-08T19:47:24Z 2025-01-03 2025-01-05T04:12:21Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/157950 Benjamin, N., Collier, S., Maloney, A. et al. Resurgence in Liouville theory. J. High Energ. Phys. 2025, 38 (2025). PUBLISHER_CC en https://doi.org/10.1007/JHEP01(2025)038 Journal of High Energy Physics Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Benjamin, Nathan Collier, Scott Maloney, Alexander Meruliya, Viraj Resurgence in Liouville theory |
| title | Resurgence in Liouville theory |
| title_full | Resurgence in Liouville theory |
| title_fullStr | Resurgence in Liouville theory |
| title_full_unstemmed | Resurgence in Liouville theory |
| title_short | Resurgence in Liouville theory |
| title_sort | resurgence in liouville theory |
| url | https://hdl.handle.net/1721.1/157950 |
| work_keys_str_mv | AT benjaminnathan resurgenceinliouvilletheory AT collierscott resurgenceinliouvilletheory AT maloneyalexander resurgenceinliouvilletheory AT meruliyaviraj resurgenceinliouvilletheory |