Entanglement Entropy in 2D non-abelian pure gauge theory

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(mgapTe−mgapT), 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.