The Schwarzian sector of higher spin CFTs

TL;DR

This paper extends the concept of the Schwarzian sector from Virasoro symmetry to higher spin conformal field theories, connecting near-extremal black hole physics with generalized Schwarzian theories and spectral analysis.

Contribution

It generalizes the Schwarzian sector to higher spin CFTs, linking near-extremal black holes with BF higher spin gravity and spectral decomposition methods.

Findings

Partition function matches BF higher spin gravity in AdS2

Spectral decomposition via 5W_N6 fusion kernel

Supersymmetric generalizations explored

Abstract

Two-dimensional conformal field theories with Virasoro symmetry generically contain a Schwarzian sector. This sector is related to the near-horizon region of the near-extremal BTZ black hole in the holographic dual. In this work we generalize this picture to CFTs with higher spin conserved currents. It is shown that the partition function in the near-extremal limit agrees with that of BF higher spin gravity in AdS$_2$ which is described by a generalized Schwarzian theory. We also provide a spectral decomposition of Schwarzian partition functions via the $\mathcal{W}_N$ fusion kernel and consider supersymmetric generalizations.