We discuss the energy flux constraints for conserved and non-conserved operators in an arbitrary higher dimensional CFT. We then consider a deep inelastic scattering thought experiment and show how to derive these and other bounds on the OPE coefficients of various operators.

We will discuss a special class of higher derivative gravity theories called Lovelock gravities, in the context of holography. For a generic Lovelock gravity in arbitrary dimensions, we will formulate the existence condition for asymptotically AdS black holes. Then, causality of the dual finite temperature CFT will be shown to impose constraints on the Lovelock parameters. Calculation of the holographic Weyl anomaly in 6+1 dimensions reveals that these constraints are completely equivalent to the ones determined by requiring positivity of the energy flux. Implications of these results on the viscosity to entropy bound will also be discussed. This talk is based on hep-th/0910.5347, 0912.1877, 0912.4244.