Spectral function of the supersymmetry current

TL;DR

This paper analyzes the spectral function of the supersymmetry current in d=3 N=2 SCFTs with gravity duals, revealing a soft gap at zero temperature and solving the gravitino equation analytically in the near-horizon limit.

Contribution

It provides the first analytic solution of the gravitino equation in the AdS_2 x R^2 background and explores the spectral function's features at zero temperature.

Findings

No Fermi surface observed.

A soft power-law gap appears at zero temperature.

Analytic solution obtained for the gravitino in AdS_2 x R^2.

Abstract

We continue our study of the retarded Green's function of the universal fermionic supersymmetry current ("supercurrent") for the most general class of d=3 N=2 SCFTs with D=10 or D=11 supergravity duals by studying the propagation of the Dirac gravitino in the electrically charged AdS-Reissner-Nordstr\"om black-brane background of N=2 minimal gauged supergravity in D=4. We expand upon results presented in a companion paper, including the absence of a Fermi surface and the appearance of a soft power-law gap at zero temperature. We also present the analytic solution of the gravitino equation in the AdS_2 X R^2 background which arises as the near-horizon limit at zero temperature. In addition we determine the quasinormal mode spectrum.