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Causality places nontrivial constraints on QFT in Lorentzian signature, for example it implies that the averaged null energy must be positive in interacting quantum field theory in flat spacetime. In conformal field theory with large central charge and a sparse spectrum, causality constraints in the Regge limit leads to a stronger energy condition which is a generalization of the averaged null energy condition. This new energy condition leads to non-trivial constraints on CFT 3-point couplings. In particular, I will also show that these constraints are consistent with the expectation that CFTs in this class, irrespective of their microscopic details, admit universal gravity-like holographic dual description. As an application of this new energy condition, I will show that any finite number of massive elementary particles with spin more than two can not interact with gravitons in AdS in a way that preserves causality. I will also explain how analogous bounds can be derived in flat spacetime by studying eikonal scattering of massive higher spin particles.

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