Resurgence in Liouville theory
Abstract 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 poin...
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SpringerOpen
2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)038 |
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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 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. |
| format | Article |
| id | doaj-art-84cdb17a563544078aa1e1fa7f269097 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-84cdb17a563544078aa1e1fa7f2690972025-01-19T12:07:17ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025114510.1007/JHEP01(2025)038Resurgence in Liouville theoryNathan Benjamin0Scott Collier1Alexander Maloney2Viraj Meruliya3Walter Burke Institute for Theoretical Physics, CaltechCenter for Theoretical Physics, Massachusetts Institute of TechnologyDepartment of Physics, McGill UniversityDepartment of Physics, McGill UniversityAbstract 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.https://doi.org/10.1007/JHEP01(2025)038Field Theories in Lower DimensionsLarge-Order Behaviour of Perturbation TheoryRenormalonsNonperturbative EffectsScale and Conformal Symmetries |
| spellingShingle | Nathan Benjamin Scott Collier Alexander Maloney Viraj Meruliya Resurgence in Liouville theory Journal of High Energy Physics Field Theories in Lower Dimensions Large-Order Behaviour of Perturbation Theory Renormalons Nonperturbative Effects Scale and Conformal Symmetries |
| 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 |
| topic | Field Theories in Lower Dimensions Large-Order Behaviour of Perturbation Theory Renormalons Nonperturbative Effects Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP01(2025)038 |
| work_keys_str_mv | AT nathanbenjamin resurgenceinliouvilletheory AT scottcollier resurgenceinliouvilletheory AT alexandermaloney resurgenceinliouvilletheory AT virajmeruliya resurgenceinliouvilletheory |