Topological R\'enyi and Entanglement Entropy for a 2d q-deformed $U(N)$   Yang-Mills theory and its Chern-Simons dual
  R\'enyi and entanglement entropies are constructed for 2d q-deformed topological Yang-Mills theories with gauge group $U(N)$, as well as the dual 3d Chern-Simons (CS) theory on Seifert manifolds. When $q=\exp[2\pi i/(N+K)]$, and $K$ is odd, the topological R\'enyi entropy and Wilson line observables of the CS theory can be expressed in terms of the modular transformation matrices of the WZW theory, $\rm{\hat{U}(N)}_{K,N(K+N)}$. If both $K$ and $N$ are odd, there is a level-rank duality of the 2d qYM theory and of the associated CS theory, as well as that of the R\'enyi and entanglement entropies, and Wilson line observables. 
Howard J. Schnitzer
hep-th cond-mat.stat-mech