Looking at supersymmetric black holes for a very long time

TL;DR

This paper analyzes correlation functions in extremal supersymmetric black holes with ${ m N}=2$ supercharges, deriving exact formulas and exploring their long-time behavior, highlighting differences from non-supersymmetric cases.

Contribution

It provides the first exact solutions for correlation functions in ${ m N}=2$ supersymmetric black holes, revealing their time-independent nature at large times.

Findings

Correlation functions approach constant values at large times.

Exact formulas for two-point functions are derived.

Supersymmetry leads to time-independent correlators, unlike non-supersymmetric cases.

Abstract

We study correlation functions for extremal supersymmetric black holes. It is necessary to take into account the strongly coupled nature of the boundary supergraviton mode. We consider the case with ${\cal N}=2$ supercharges which is the minimal amount of supersymmetry needed to give a large ground state degeneracy, separated from the continuum. Using the exact solution for this theory we derive formulas for the two point function and we also give integral expressions for any $n$-point correlator. These correlators are time independent at large times and approach constant values that depend on the masses and couplings of the bulk theory. We also explain that in the non-supersymmetric case, the correlators develop a universal time dependence at long times. This paper is the longer companion paper of arXiv:2207.00407.