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Abstract

We evaluate the Average Null Energy Condition (ANEC) on momentum eigenstates
generated by the stress tensor in perturbative $\lambda \, \phi^4$ and general
spacetime dimension. We first compute the norm of the stress-tensor state at
second order in $\lambda$; as a by-product of the derivation we obtain the full
expression for the stress tensor 2-point function at this order. We then
compute the ANEC expectation value to first order in $\lambda$, which also
depends on the coupling of the stress-tensor improvement term $\xi$. We study
the bounds on these couplings that follow from the ANEC and unitarity at first
order in perturbation theory. These bounds are stronger than unitarity in some
regions of coupling space.