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 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 fourpoint function in an explicit compact form. Next, we demonstrate its equivalence to a conformal block expansion, revealing an explicit but nonlocal 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2024
 DOI:
 10.48550/arXiv.2407.11124
 arXiv:
 arXiv:2407.11124
 Bibcode:
 2024arXiv240711124S
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 30 pages, 3 figures