The study of topological phases, topological field theory, and topology itself is richer in higher dimensions. In this talk I will discuss aspects of a bulk/edge correspondence that exists in all dimensions. Focusing on systems described by Abelian p-form gauge theories I will illustrate the existence of an infinite-dimensional higher-form current algebra existing at the system’s edge. This is an analogue to the Kac-Moody algebra arising at the edge of (2+1)-dimensional topological phases. I will then describe the “edge-mode” theory carrying this current algebra: a pair of higher-form Maxwell theories tied together by a novel boundary condition. When this edge appears as part of an “entangling cut,” the existence of this current algebra completely determines the entanglement entropy and its subleading, universal, contributions in all dimensions and for cuts of arbitrary topology.