R\'enyi Entropy for a $\bf 2d$ CFT with a gauge field: $\bf \widehat{\rm SU}(N)_1$ WZW theory on a branched torus

Abstract

The R\'enyi entropy for the $\widehat{\rm SU}(N)_1$ WZW model as described by $N$ free fermions coupled to a $U(1)$ constraint field is computed on an $n$-sheeted branched torus. The boundary condition of the harmonic component of the gauge field on the homology cycles of the genus $g$ Riemann surface is central to the final result. This calculation is complementary to that of arXiv:$1510.05993$, which presents the bose side of the bose-fermi equivalence.