On universality of stress-energy tensor correlation functions in supergravity

TL;DR

The paper addresses the universality of boundary stress-energy tensor correlators in strongly coupled finite-temperature gauge theories realized via holography. Using the Minkowski-space AdS/CFT prescription, it computes the retarded two-point function of the boundary stress-energy tensor in a broad class of type IIB supergravity backgrounds with regular horizons and shows a universal, horizon-area–driven form in the low-energy limit, leading to $G^{R}_{12,12}(7,0) = -\frac{i\omega s}{4\pi} \left(1 + \mathcal{O}\left(\frac{\omega}{T}\right)\right)$ with $s = \mathcal{A}_8/(4 V_3 G_N)$. Via the fluctuation-dissipation theorem and the Kubo relation, the universal shear viscosity to entropy density ratio $\eta/s = 1/(4\pi)$ is recovered, and connections to universal low-energy absorption cross-sections for minimally coupled scalars are drawn. The analysis extends to black brane geometries with non-spherical horizons that satisfy $R_t^t - R_\alpha^\alpha = 0$, clarifying the precise conditions under which this universality holds and highlighting the horizon data as the source of universal transport properties in holographic plasmas.

Abstract

Using the Minkowski space AdS/CFT prescription we explicitly compute in the low-energy limit the two-point correlation function of the boundary stress-energy tensor in a large class of type IIB supergravity backgrounds with a regular translationally invariant horizon. The relevant set of supergravity backgrounds includes all geometries which can be interpreted via gauge theory/string theory correspondence as being holographically dual to finite temperature gauge theories in Minkowski space-times. The fluctuation-dissipation theorem relates this correlation function computation to the previously established universality of the shear viscosity from supergravity duals, and to the universality of the low energy absorption cross-section for minimally coupled massless scalars into a general spherically symmetric black hole. It further generalizes the latter results for the supergravity black brane geometries with non-spherical horizons.