Abstract:
Causality in conformal field theory is encoded in the averaged null energy condition (ANEC). I will describe three recent applications and extensions of this idea, to holography, non-conformal QFTs, and hydrodynamics. Similar arguments, in these three different settings, lead to constraints on the geodesic length spectrum in quantum gravity, the coupling constants of irrelevant operators in effective field theory, and transport coefficients in finite-temperature systems.