Relative entropy for $λϕ^4$ in the Rindler wedge

Abstract

We consider the relative entropy between the vacuum and a coherent state in the Rindler wedge for an interacting $λϕ^4$ theory to first order in $λ$. We construct the perturbatively interacting Weyl algebra of the wedge, and employ Tomita--Takesaki modular theory and the Araki--Uhlmann formula to compute the relative entropy. We verify that the relative entropy reduces to the classical (interacting) boost Noether charge, analogously to the free theory, and that the Bekenstein bound holds.