Holographic stress tensor at finite coupling

TL;DR

This work provides a unified holographic framework to compute the stress tensor and its two- and three-point functions for arbitrary higher-derivative gravity theories with Lagrangians of the form ${\mathcal L}(g^{ab}, R_{abcd}, \nabla_e R_{abcd})$. Using the first law of entanglement and a background-field expansion, it derives concise expressions for the one-, two-, and three-point functions, tying the normalization to ${\mathcal C}_T$ and connecting B-type trace anomalies to these correlators in even dimensions. The analysis systematically incorporates ${\nabla R}$ corrections, showing how they shift effective curvature couplings ($c_6'$, etc.) and thereby modify anomaly coefficients and correlator data. The paper also applies the formalism to compute the shear viscosity to entropy density ratio $\eta/s$ in various four-derivative theories, finding that, within energy-positivity and causality constraints, $\eta/s$ can be driven very small, with explicit bounds for Weyl-squared and Weyl-cubed theories. Overall, the results establish a transparent link between bulk higher-derivative couplings, holographic anomalies, and stress-tensor correlators, with implications for finite-coupling holography and plasma dynamics.

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 $η/s$ for holographic plasmas is less than the KSS bound.

Figures (1)

• Figure 1: $\lambda$ vs $\mu$ plot. The horizontal line corresponds to $\mu=0$. $(\eta/s)_{min}=0.55/4\pi$ for $\mu=0$ and $(\eta/s)_{min}=0.17/4\pi$ for $\mu\neq 0$.