A universal Schwarzian sector in two-dimensional conformal field theories

TL;DR

This paper demonstrates that a broad class of two-dimensional conformal field theories inherently contain a Schwarzian sector, which governs low-temperature dynamics and correlators, with implications for holography and black hole physics.

Contribution

The authors identify a universal Schwarzian sector in 2D CFTs with large central charge, independent of holographic duals, using bootstrap methods and connecting to near-extremal black hole geometries.

Findings

Density of states and correlators are governed by the Schwarzian theory at low temperature.

Out-of-time-order correlators are computed in a controlled approximation.

Results have a gravitational interpretation in terms of near-extremal rotating BTZ black holes.

Abstract

We show that an extremely generic class of two-dimensional conformal field theories (CFTs) contains a sector described by the Schwarzian theory. This applies to theories with no additional symmetries and large central charge, but does not require a holographic dual. Specifically, we use bootstrap methods to show that in the grand canonical ensemble, at low temperature with a chemical potential sourcing large angular momentum, the density of states and correlation functions are determined by the Schwarzian theory, up to parametrically small corrections. In particular, we compute out-of-time-order correlators in a controlled approximation. For holographic theories, these results have a gravitational interpretation in terms of large, near-extremal rotating BTZ black holes, which have a near horizon throat with nearly AdS$_2 \times S^1$ geometry. The Schwarzian describes strongly coupled gravitational dynamics in the throat, which can be reduced to Jackiw-Teitelboim (JT) gravity interacting with a $U(1)$ field associated to transverse rotations, coupled to matter. We match the physics in the throat to observables at the AdS$_3$ boundary, reproducing the CFT results.