Shockwaves from OPE and causality
Abstract: Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In conformal field theory, I will describe the operator product expansion in the Regge limit, and show that the leading contribution is exactly the shockwave operator. Consequently, I will show that causality implies that the averaged null energy must be positive in interacting quantum field theory in flat spacetime. Whereas, for large-N CFTs, causality constraints in the Regge limit leads to a stronger condition which is the CFT version of the gravity condition proposed by Engelhardt and Fischetti. This causality condition leads to strong constraints on CFT 3-point couplings. In particular, I will also show that in four-dimensions, conformal field theories with large-N and a sparse spectrum exhibit universal, gravity-like behavior and the anomaly coefficients satisfy a=c.