  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.
