ANEC in $\lambda \, \phi^4$ theory

Abstract

Motivated by the goal of applying the average null energy condition (ANEC) to renormalisation group flows, we calculate in $\lambda \phi^4$ theory the expectation value of the ANEC operator in a particular scalar state perturbatively up to third order in the quartic coupling and verify the expected CFT answer. The work provides the technical tools for studying the expectation value of the ANEC operator in more interesting states, for example tensorial states relevant to the Hofman-Maldacena collider bounds, away from critical points.