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

TL;DR

This paper computes the expectation value of the ANEC operator in $lambda phi^4$ theory up to third order, providing tools for studying energy conditions in quantum field theories and conformal field theories.

Contribution

It offers a perturbative calculation of the ANEC expectation value in $lambda phi^4$ theory and develops methods applicable to more complex states and non-critical points.

Findings

Verification of the expected CFT result for ANEC in $lambda phi^4$ theory

Perturbative calculation up to third order in coupling

Development of techniques for analyzing ANEC in tensorial and non-critical states

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.