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We explore the constraints imposed on higher curvature corrections of theLovelock type due to causality restrictions in the boundary of asymptoticallyAdS space-time. In the framework of AdS/CFT, this is related to positivity ofthe energy constraints that arise in conformal collider physics. We presentexplicit analytic results that fully address these issues for cubic Lovelockgravity in arbitrary dimensions and give the formal analytic results thatcomprehend general Lovelock theory. The computations can be performed in twoways, both by considering a thermal setup in a black hole background and bystudying the scattering of gravitons with a shock wave in AdS. We show thatboth computations coincide in Lovelock theory. The different helicities, asexpected, provide the boundaries defining the region of allowed couplings. Wegeneralize these results to arbitrary higher dimensions and discuss theirconsequences on the shear viscosity to energy density ratio of CFT plasmas, thepossible existence of Boulware-Deser instabilities in Lovelock theory and theextent to which the AdS/CFT correspondence might be valid for arbitrarydimensions.

Causality in AdS/CFT and Lovelock theory