Lovelock theories, holography and the fate of the viscosity bound

TL;DR

This paper investigates Lovelock gravity theories within the AdS/CFT framework, revealing new causality and stability constraints, and analyzing shear viscosity bounds across various dimensions, with implications for the dual conformal field theories.

Contribution

It uncovers interior causality violations and instabilities in Lovelock theories, providing new constraints and a detailed analysis of shear viscosity bounds in diverse dimensions.

Findings

Causality violation can occur deep inside the geometry.

Instabilities can appear at any point in the geometry.

Shear viscosity to entropy density ratio behaves smoothly with dimension.

Abstract

We consider Lovelock theories of gravity in the context of AdS/CFT. We show that, for these theories, causality violation on a black hole background can occur well in the interior of the geometry, thus posing more stringent constraints than were previously found in the literature. Also, we find that instabilities of the geometry can appear for certain parameter values at any point in the geometry, as well in the bulk as close to the horizon. These new sources of causality violation and instability should be related to CFT features that do not depend on the UV behavior. They solve a puzzle found previously concerning unphysical negative values for the shear viscosity that are not ruled out solely by causality restrictions. We find that, contrary to previous expectations, causality violation is not always related to positivity of energy. Furthermore, we compute the bound for the shear viscosity to entropy density ratio of supersymmetric conformal field theories from d=4 till d=10 - i.e., up to quartic Lovelock theory -, and find that it behaves smoothly as a function of d. We propose an approximate formula that nicely fits these values and has a nice asymptotic behavior when d goes to infinity for any Lovelock gravity. We discuss in some detail the latter limit. We finally argue that it is possible to obtain increasingly lower values for the shear viscosity to entropy density ratio by the inclusion of more Lovelock terms.