Quantum chaos in Liouville CFT
Abstract Fast scrambling is a distinctive feature of quantum gravity, which by means of holography is closely tied to the behaviour of large-c conformal field theories. We study this phenomenon in the context of semiclassical Liouville theory, providing both insights into the mechanism of scrambling...
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SpringerOpen
2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)017 |
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| author | Julian Sonner Benjamin Strittmatter |
| author_facet | Julian Sonner Benjamin Strittmatter |
| author_sort | Julian Sonner |
| collection | DOAJ |
| description | Abstract Fast scrambling is a distinctive feature of quantum gravity, which by means of holography is closely tied to the behaviour of large-c conformal field theories. We study this phenomenon in the context of semiclassical Liouville theory, providing both insights into the mechanism of scrambling in CFTs and into the structure of Liouville theory, finding that it exhibits a maximal Lyapunov exponent despite not featuring the identity in its spectrum. However, as we show, the states contributing to the relevant correlation function can be thought of as dressed scramblons. At a technical level we first use the path integral picture in order to derive the Euclidean four-point function in an explicit compact form. Next, we demonstrate its equivalence to a conformal block expansion, revealing an explicit but non-local map between path integral saddles and conformal blocks. By analytically continuing both expressions to Lorentzian times, we obtain two equivalent formulations of the OTOC, which we use to study the onset of chaos in Liouville theory. We take advantage of the compact form in order to extract a Lyapunov exponent and a scrambling time. From the conformal block expansion formulation of the OTOC we learn that scrambling shifts the dominance of conformal blocks from heavy primaries at early times to the lightest primary at late times. Finally, we discuss our results in the context of holography. |
| format | Article |
| id | doaj-art-4ff0db230afa47bd86a5dc752cc6ff44 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-4ff0db230afa47bd86a5dc752cc6ff442025-08-20T02:30:49ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025513010.1007/JHEP05(2025)017Quantum chaos in Liouville CFTJulian Sonner0Benjamin Strittmatter1Department of Theoretical Physics, University of GenevaDepartment of Theoretical Physics, University of GenevaAbstract Fast scrambling is a distinctive feature of quantum gravity, which by means of holography is closely tied to the behaviour of large-c conformal field theories. We study this phenomenon in the context of semiclassical Liouville theory, providing both insights into the mechanism of scrambling in CFTs and into the structure of Liouville theory, finding that it exhibits a maximal Lyapunov exponent despite not featuring the identity in its spectrum. However, as we show, the states contributing to the relevant correlation function can be thought of as dressed scramblons. At a technical level we first use the path integral picture in order to derive the Euclidean four-point function in an explicit compact form. Next, we demonstrate its equivalence to a conformal block expansion, revealing an explicit but non-local map between path integral saddles and conformal blocks. By analytically continuing both expressions to Lorentzian times, we obtain two equivalent formulations of the OTOC, which we use to study the onset of chaos in Liouville theory. We take advantage of the compact form in order to extract a Lyapunov exponent and a scrambling time. From the conformal block expansion formulation of the OTOC we learn that scrambling shifts the dominance of conformal blocks from heavy primaries at early times to the lightest primary at late times. Finally, we discuss our results in the context of holography.https://doi.org/10.1007/JHEP05(2025)017AdS-CFT CorrespondenceField Theories in Lower DimensionsScale and Conformal Symmetries |
| spellingShingle | Julian Sonner Benjamin Strittmatter Quantum chaos in Liouville CFT Journal of High Energy Physics AdS-CFT Correspondence Field Theories in Lower Dimensions Scale and Conformal Symmetries |
| title | Quantum chaos in Liouville CFT |
| title_full | Quantum chaos in Liouville CFT |
| title_fullStr | Quantum chaos in Liouville CFT |
| title_full_unstemmed | Quantum chaos in Liouville CFT |
| title_short | Quantum chaos in Liouville CFT |
| title_sort | quantum chaos in liouville cft |
| topic | AdS-CFT Correspondence Field Theories in Lower Dimensions Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP05(2025)017 |
| work_keys_str_mv | AT juliansonner quantumchaosinliouvillecft AT benjaminstrittmatter quantumchaosinliouvillecft |