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Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity

We explore the relation between positivity of the energy constraints in conformal field theories and causality in their dual gravity description. Our discussion involves CFTs with different central charges whose description, in the gravity side, requires the inclusion of quadratic curvature corrections. It is enough, indeed, to consider the Gauss-Bonnet term. We find that both sides of the AdS/CFT correspondence impose a restriction on the Gauss-Bonnet coupling. In the case of 6d supersymmetric CFTs, we show the full matching of these restrictions. We perform this computation in two ways. First by considering a thermal setup in a black hole background. Second by scrutinizing the scattering of gravitons with a shock wave in AdS. The different helicities provide the corresponding lower and upper bounds. We generalize these results to arbitrary higher dimensions and comment on some hints and puzzles they prompt regarding the possible existence of higher dimensional CFTs and the extent to which the AdS/CFT correspondence would be valid for them.