Causality in AdS/CFT and Lovelock theory

TL;DR

This paper investigates how causality constraints in AdS/CFT limit higher curvature corrections in Lovelock gravity, providing explicit analytic results for cubic Lovelock gravity and implications for CFT plasma properties.

Contribution

It offers the first comprehensive analytic analysis of causality constraints on Lovelock gravity in arbitrary dimensions within the AdS/CFT framework.

Findings

Causality bounds restrict Lovelock coupling constants.

Results apply to black hole backgrounds and graviton scattering in AdS.

Implications for shear viscosity and stability of Lovelock theories.

Abstract

We explore the constraints imposed on higher curvature corrections of the Lovelock type due to causality restrictions in the boundary of asymptotically AdS space-time. In the framework of AdS/CFT, this is related to positivity of the energy constraints that arise in conformal collider physics. We present explicit analytic results that fully address these issues for cubic Lovelock gravity in arbitrary dimensions and give the formal analytic results that comprehend general Lovelock theory. The computations can be performed in two ways, both by considering a thermal setup in a black hole background and by studying the scattering of gravitons with a shock wave in AdS. We show that both computations coincide in Lovelock theory. The different helicities, as expected, provide the boundaries defining the region of allowed couplings. We generalize these results to arbitrary higher dimensions and discuss their consequences on the shear viscosity to energy density ratio of CFT plasmas, the possible existence of Boulware-Deser instabilities in Lovelock theory and the extent to which the AdS/CFT correspondence might be valid for arbitrary dimensions.