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

Abstract

Rényi 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 Rényi entropy and Wilson line observables of the CS theory can be expressed in terms of the modular transformation matrices of the WZW theory, ${\hat{\mathrm{U}}(\mathrm{N})}_{\mathrm{K},\mathrm{N}(\mathrm{K}+\mathrm{N})}$. 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 Rényi and entanglement entropies, and Wilson line observables.

10 pages

References in corpus (11)

• Aspects of Entanglement Entropy for Gauge Theories
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories
• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• The entanglement of distillation for gauge theories
• Entanglement entropy for a Maxwell field: Numerical calculation on a two dimensional lattice
• Entanglement entropy of a Maxwell field on the sphere
• Entanglement entropy in d+1 SU(N) gauge theory
• Notes on Entanglement in Abelian Gauge Theories
• Entanglement Entropy in 2D Non-abelian Pure Gauge Theory
• Left-Right Entanglement Entropy, D-Branes, and Level-rank duality

Cited by in corpus (1)

• Comments on Defining Entanglement Entropy