Quantum chaos in Liouville CFT

Article Article scientifique Article Quantum chaos in Liouville CFT eng 2025-05-02 2025 author Sonner Julian U. Geneva (main) 843498 Département de physique théorique (FITEO) author Strittmatter Benjamin Bogdan U. Geneva (main) 928725 10.1007/jhep05(2025)017 1029-8479 2407.11124 https://link.springer.com/10.1007/JHEP05(2025)017 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. AdS-CFT Correspondence Field Theories in Lower Dimensions Scale and Conformal Symmetries Dewey 500.2 37 Département de physique théorique 133 false The journal of high energy physics 05 5 b3eea496-5232-405b-974e-94c26d041b6f Article (Published version) Public Article_scientifique_from_crossref.pdf 2178573 application/pdf CC BY-4.0 7cda5804dbc2a48142b11d4cca4e0483721780c3df9f2243652812207927a9d1 openAccess Faculté des sciences / Section de physique / Département de physique théorique

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Strittmatter, Benjamin Bogdan