Abstract
We extend the holographic Schwinger-Keldysh prescription introduced in [1] to charged black branes, with a view towards studying Hawking radiation in these backgrounds. Equivalently we study the 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 [2]. The Schwinger-Keldysh correlators derived using this prescription automatically satisfy the appropriate KMS relations with Fermi-Dirac factors.
Highlights
JHEP03(2021)233 copies of RN-AdS black brane exteriors which we will term as the RN-SK saddle/geometry. that generalises grSK geometry
In this note we extended the prescription for gravitational Schwinger-Keldysh saddles to the case of charged black branes
This geometry is dual to the real-time evolution of a CFT
Summary
We will describe how to construct Hawking modes in charged black branes when the ingoing quasi-normal modes are known. The answer to this conundrum lies in the fact that, by the standard rules of AdS/CFT, the boundary symmetries can always be composed with bulk gauge symmetries (since they act trivially on the Hilbert space of states of the CFT) Having implemented the boundary CP T in the bulk, we will use this symmetry to generate new solutions to the bulk field equations linearised about the RN-AdS background. To see how this is done, let us begin with the simplest example of a complex scalar field with charge q probing the RN-AdS black brane. As we will argue below, this factor is crucial to how the RN-SK geometry gets the physics of Hawking radiation right
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