Absence of a Fermi surface in classical minimal four-dimensional gauged supergravity

TL;DR

This paper shows that in a specific four-dimensional supergravity setting, the expected Fermi surface signature is absent in the supercurrent two-point function, challenging assumptions about fermionic behavior in such backgrounds.

Contribution

It introduces a novel analysis method using ingoing Eddington-Finkelstein coordinates to study gravitino correlators, revealing the absence of a Fermi surface in this context.

Findings

No Fermi surface singularity in the supercurrent correlator.

Method confirms previous results for massless charged Dirac fields.

Provides new insights into fermionic responses in supergravity backgrounds.

Abstract

We demonstrate that the two point function of the supercurrent dual to the gravitino in the four-dimensional extremal anti-de Sitter Reissner-Nordstrom black hole does not exhibit a Fermi surface singularity. In our analysis, we utilize the ingoing Eddington-Finkelstein coordinate system, which enables us to bypass certain complications in the determination of the allowed near horizon behavior of the gravitino field at zero frequency. We check that our method agrees with previous results for the massless charged Dirac field.