Theory HEP Seminar

Entanglement, edge states, and gauge symmetry

William Donnelly

University of Waterloo

The entanglement entropy associated to a region of space is a quantity that plays an important role in several areas of theoretical physics, including black hole thermodynamics, condensed matter theory and the AdS/CFT correspondence. In gauge theory the Hilbert space is not a simple tensor product between two regions of space, so it is not clear how to define the entanglement entropy. I will show that associating Hilbert spaces to spatial regions in gauge theory requires introducing edge states of the kind that appear in 2+1 gravity and quantum Hall systems. The gauge symmetry acts nontrivially on the edge states, allowing for a decomposition of the entanglement entropy into the sum of a bulk part, and a part computable purely from boundary correlators. I will illustrate this decomposition explicitly in lattice gauge theory, and give several examples in which we find that the boundary part of the entropy dominates.