Supersymmetric Black Holes and the SJT/nSCFT${}_1$ Correspondence

Abstract

We consider 1/4 BPS black hole solutions of $\mathcal{N}=2$ gauged supergravity in $Ad{S}_4$. The near horizon geometry is $Ad{S}_2\times S^2$ and supersymmetry is enhanced. In the first part of the paper we choose a moment map, which allows the embedding of this supergravity solution into a sugra theory with a hypermultiplet. We then perform the s-wave reduction of this theory at the horizon and determine the dilaton multiplet, which couples to both metric and gravitino fluctuations. In the second part we work with Euclidean axial $\mathcal{N}=(2,2)$ JT supergravity and show how to add gauged matter in form of covariantly twisted chiral and anti-chiral multiplets. We demonstrate how to reduce the on-shell action to boundary superspace. We compare both theories and calculate the fourpoint function by integrating out gravitons, gravitini and photons for the s-wave setting and by use of the Super-Schwarzian modes in the JT theory.

45 pages, v2: references and comments added, minor corrections, version accepted for publication