Positive Energy Conditions in 4D Conformal Field Theory

Understand

We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality $\langle T^{00} \rangle \ge -C/L^4$, where $L$ is the size of the smearing region, and $C$ is a positive constant that depends on the theory.

• If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies.
• We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory.
• The constraints we find are weaker than the "conformal collider" constraints of Hofman and Maldacena.