AdS_7/CFT_6, Gauss-Bonnet Gravity, and Viscosity Bound

TL;DR

This paper explores the relationship between causality, energy positivity, and viscosity bounds in Gauss-Bonnet gravity within an AdS_7 background, establishing bounds on the coupling and viscosity/entropy ratio through holographic methods.

Contribution

It provides a precise connection between causality, energy positivity, and viscosity bounds in six-dimensional CFTs via holography and Gauss-Bonnet gravity.

Findings

Bound on Gauss-Bonnet coupling from causality

Relation between energy flux parameters and Weyl anomaly

New viscosity/entropy ratio bound

Abstract

We study the relation between the causality and the positivity of energy bounds in Gauss-Bonnet gravity in AdS_7 background and find a precise agreement. Requiring the group velocity of metastable states to be bounded by the speed of light places a bound on the value of Gauss-Bonnet coupling. To find the positivity of energy constraints we compute the parameters which determine the angular distribution of the energy flux in terms of three independent coefficients specifying the three-point function of the stress-energy tensor. We then relate the latter to the Weyl anomaly of the six-dimensional CFT and compute the anomaly holographically. The resulting upper bound on the Gauss-Bonnet coupling coincides with that from causality and results in a new bound on viscosity/entropy ratio.