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Quantum Chaos in Liouville CFT

Julian Sonner, Benjamin Strittmatter

15/7/24 Published in : arXiv:2407.11124

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 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.

Entire article

Phase I & II research project(s)

  • String Theory

Phase III direction(s)

  • Holography and bulk-boundary correspondence

Cartan Geometry and Infinite-Dimensional Kempf-Ness Theory

Matrix models for extremal and integrated correlators of higher rank

  • Leading house

  • Co-leading house


The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

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