Supersymmetric Black Holes and the SJT/nSCFT$_1\!$ Correspondence

TL;DR

This paper explores 1/4 BPS black hole solutions in ${ m AdS}_4$ supergravity, their near-horizon geometry, and establishes a correspondence with supersymmetric Jackiw-Teitelboim (JT) supergravity, analyzing boundary correlators and matter couplings.

Contribution

It introduces a method to embed ${ m AdS}_4$ black holes into supergravity with hypermultiplets and connects this to Euclidean JT supergravity, providing new insights into boundary dynamics and correlators.

Findings

Derived the s-wave reduction of supergravity solutions at the horizon.

Demonstrated how to incorporate gauged matter into Euclidean JT supergravity.

Calculated four-point functions using both supergravity and super-Schwarzian modes.

Abstract

We consider 1/4 BPS black hole solutions of ${\cal N}=2$ gauged supergravity in $AdS_4$. The near horizon geometry is $AdS_2 \times S^2$ 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.