Entanglement entropy in d+1 SU(N) gauge theory

Abstract

We consider the entanglement entropy for a sub-system in d+1 dimensional SU(N) lattice gauge theory. The 1+1 gauge theory is treated exactly and shows trivial behavior. Gauge theories in higher dimensions are treated within Migdal-Kadanoff approximation. We consider the gauge theory in the confinement phase. We demonstrate the existence of a non-analytical change from the short distance to long distance form in the entanglement entropy in such systems (d>2) reminiscent of a phase transition. The transition is manifested in nontrivial change in the RG flow of the character expansion coefficients defining the partition function.

9 pages, 5 figures, revised version: one figure added, discussion of the results extended, misprints corrected

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