Abstract
The Rényi entropy for the SUˆ(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.