The Schwarzian sector of higher spin CFTs

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 AdS2 which is described by a generalized Schwarzian theory. We also provide a spectral decomposition of Schwarzian partition functions via the $$ {\mathcal{W}}_N $$ W N fusion kernel and consider supersymmetric generalizations.

Supergroup Structure of Jackiw-Teitelboim Supergravity

“…In particular, this holds for SL(N, R), where (α, α) = 2. However, the equation that one finds by taking the Schwarzian/JT limit of the W N character yields (see, e.g., [116]):…”

AdS3/AdS2 degression of massless particles

“…In particular, the equivalence of 2d and 3d partition functions of higher-spin fields in the near-horizon region of the near-extremal BTZ black hole was recently shown in[46].…”

Higher spin wormholes from modular bootstrap

“…The results of this work and that of [54] provide information about the one-and twopoint functions Z(τ ) and Z(τ 1 )Z(τ 2 ) for the low-temperature regime of pure higher spin gravity in 3-dimensions. This is the near-horizon regime of near-extremal black holes in which an AdS 2 -throat appears [55].…”

“…12 [17,54,55]. 1 Before we carry out the procedure outlined above for irrational CFTs with W N symmetries, we describe some essential ingredients that will be useful.…”