Lovelock theories, holography and the fate of the viscosity bound

TL;DR

This work analyzes shear viscosity in AdS/CFT with Lovelock gravity, showing that causality and stability constraints extend into the bulk and can tightly bound η/s beyond boundary considerations. By computing C_T and the three-point function parameters t_2 and t_4, the authors establish consistency with positivity of energy bounds and reveal t_4 = 0 across Lovelock theories. They demonstrate that while higher-order Lovelock terms can lower η/s, bulk causality and instabilities prevent arbitrarily small values at fixed dimension, though no dimension-independent bound emerges; in the large-d limit with many Lovelock terms, η/s can approach zero in principle. The results provide nontrivial checks of AdS/CFT in non-Einstein gravities and suggest rich structure for dual CFTs in higher dimensions, with implications for transport and stability.

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.