Holographic stress tensor at finite coupling

TL;DR

This paper computes holographic stress tensor correlation functions for general higher derivative gravity theories, relating them to trace anomalies and the central charge ${ m C}_T$, with applications to holographic plasma viscosity bounds.

Contribution

It provides a general method to calculate stress tensor correlators in higher derivative gravity duals and links these to trace anomalies and ${ m C}_T$ in arbitrary dimensions.

Findings

Derived the proportionality constant with B-type trace anomaly.

Computed two and three point functions for stress tensors in general higher derivative theories.

Applied results to cases where shear viscosity to entropy ratio is below the KSS bound.

Abstract

We calculate one, two and three point functions of the holographic stress tensor for any bulk Lagrangian of the form ${\mathcal{L}}(g^{ab}, R_{abcd}, \nabla_e R_{abcd})$. Using the first law of entanglement, a simple method has recently been proposed to compute the holographic stress tensor arising from a higher derivative gravity dual. The stress tensor is proportional to a dimension dependent factor which depends on the higher derivative couplings. In this paper, we identify this proportionality constant with a B-type trace anomaly in even dimensions for any bulk Lagrangian of the above form. This in turn relates to ${\mathcal{C}}_T$, the coefficient appearing in the two point function of stress tensors. We use a background field method to compute the two and three point function of stress tensors for any bulk Lagrangian of the above form in arbitrary dimensions. As an application we consider general situations where $\eta/s$ for holographic plasmas is less than the KSS bound.