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

Abstract

We demonstrate that the two point function of the supercurre nt dual to the gravitino in the four-dimensional extremal anti-de Sit ter Reissner-Nordstrom black hole does not exhibit a Fermi surface singularity. In our ana lysis, we utilize the ingoing Eddington-Finkelstein coordinate system, which enables u s to bypass certain complications in the determination of the allowed near horizon behavior of the gravitino field at zero fre- quency. We check that our method agrees with previous result s for the massless charged Dirac field.