The edge of entanglement: getting the boundary right for non-minimally coupled scalar fields

In entanglement computations for a free scalar field with coupling to background curvature, there is a boundary term in the modular hamiltonian which must be correctly specified in order to get sensible results. we focus here on the entanglement in flat space across a planar interface and (in the case of conformal coupling) other geometries related to this one by weyl rescaling of the metric. for these “half-space entanglement” computations, we give a new derivation of the boundary term and revisit how it clears up a number of puzzles in the literature, including mass corrections and twist operator dimensions. we also discuss how related boundary terms show up in other field theories.