Entanglement Entropy in 2D Non-abelian Pure Gauge Theory

Abstract

We compute the Entanglement Entropy (EE) of a bipartition in 2D pure non-abelian $U(N)$ gauge theory. We obtain a general expression for EE on an arbitrary Riemann surface. We find that due to area-preserving diffeomorphism symmetry EE does not depend on the size of the subsystem, but only on the number of disjoint intervals defining the bipartition. In the strong coupling limit on a torus we find that the scaling of the EE at small temperature is given by $S(T)-S(0)=O\left(\frac{m_{gap}}{T}{e}^{-\frac{m_{gap}}{T}}\right)$, which is similar to the scaling for the matter fields recently derived in literature. In the large $N$ limit we compute all of the Renyi entropies and identify the Douglas-Kazakov phase transition.

6 pages

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Cited by in corpus (5)

• Notes on Entanglement in Abelian Gauge Theories
• Conformal perturbation theory and higher spin entanglement entropy on the torus
• Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization
• Entanglement Witnessing for Lattice Gauge Theories
• Entanglement entropy and edge modes in topological string theory: I