Holographic KMS relations at finite density

TL;DR

This paper extends the holographic Schwinger-Keldysh framework to charged black branes, enabling the study of real-time correlators at finite density and temperature, and confirms the KMS relations for fermionic fields.

Contribution

It introduces a holographic prescription for real-time correlators in charged black brane backgrounds, verifying KMS relations for fermionic probes at finite density.

Findings

Derived Schwinger-Keldysh correlators satisfy KMS relations with Fermi-Dirac factors.

Extended the Dirac equation solutions in a boundary derivative expansion.

Validated the prescription using charged Dirac probe fields.

Abstract

We extend the holographic Schwinger-Keldysh prescription introduced in arXiv:1812.08785 to charged black branes, with a view towards studying Hawking radiation in these backgrounds. Equivalently we study real-time fluctuations of the dual CFT held at finite temperature and finite chemical potential. We check our prescription using charged Dirac probe fields. We solve the Dirac equation in a boundary derivative expansion extending the results in arXiv:2011.07039. The Schwinger-Keldysh correlators derived using this prescription automatically satisfy the appropriate KMS relations with Fermi-Dirac factors.