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arXiv · 1605.08075

Topological R\'enyi and Entanglement Entropy for a 2d q-deformed $U(N)$ Yang-Mills theory and its Chern-Simons dual

Howard J. Schnitzer
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Abstract

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.

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Howard J. Schnitzer. 2016-05-25. Topological R\'enyi and Entanglement Entropy for a 2d q-deformed $U(N)$ Yang-Mills theory and its Chern-Simons dual. https://arxiv.org/abs/1605.08075

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