AdS_7/CFT_6, Gauss-Bonnet Gravity, and Viscosity Bound

We study the relation between the causality and the positivity of energy bounds in Gauss-Bonnet gravity in AdS_7 background and find a precise agreement. Requiring the group velocity of metastable states to be bounded by the speed of light places a bound on the value of Gauss-Bonnet coupling. To find the positivity of energy constraints we compute the parameters which determine the angular distribution of the energy flux in terms of three independent coefficients specifying the three-point function of the stress-energy tensor. We then relate the latter to the Weyl anomaly of the six-dimensional CFT and compute the anomaly holographically. The resulting upper bound on the Gauss-Bonnet coupling coincides with that from causality and results in a new bound on viscosity/entropy ratio.