The Schwarzian sector of higher spin CFTs

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 WN fusion kernel and consider supersymmetric generalizations.

Automated summary

This study extends the concept of the Schwarzian sector in two-dimensional conformal field theories to CFTs with higher spin conserved currents, showing the agreement of partition functions in the near-extremal limit with BF higher spin gravity in AdS(2). The spectral decomposition of Schwarzian partition functions is provided via the WN fusion kernel, along with considerations of supersymmetric generalizations.