8/31/2023 0 Comments Renyi entropyStevan, Knot invariants, Chern-Simons theory and the topological recursion, Ph.D. Mariño, Torus knots and mirror symmetry, Annales Henri Poincaré 13 (2012) 1873. Stevan, Chern-Simons invariants of torus links, Annales Henri Poincaré 11 (2010) 1201. Sharma, Multi-boundary entanglement in Chern-Simons theory with finite gauge groups, JHEP 04 (2020) 158. Radhakrishnan, Galois conjugation and multiboundary entanglement entropy, JHEP 12 (2020) 045. Dhara, Entanglement on multiple S 2 boundaries in Chern-Simons theory, JHEP 08 (2019) 034. Prudenziati, Circuit complexity of knot states in Chern-Simons theory, JHEP 07 (2019) 163. Morozov, From Topological to Quantum Entanglement, JHEP 05 (2020) 116. Zhou, Linking entanglement and discrete anomaly, JHEP 05 (2018) 008. Parrikar, Entanglement entropy and the colored Jones polynomial, JHEP 05 (2018) 038. Joshi, Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups, JHEP 02 (2018) 163. Parrikar, Multi-boundary entanglement in Chern-Simons theory and link invariants, JHEP 04 (2017) 061. Witten, Quantum field theory and the Jones polynomial, Commun. Nowling, Topological entanglement entropy in Chern-Simons theories and quantum Hall fluids, JHEP 05 (2008) 016. Wen, Detecting topological order in a ground state wave function, Phys. Preskill, Topological entanglement entropy, Phys. We also analyze the Rényi entropies of T p,pn link in the double scaling limit of k → ∞ and n → ∞ and propose that the entropies converge in the double limit as well. Further, the universal parts appearing in the large k limits of the entanglement entropy and the minimum Rényi entropy for torus links T p,pn can be interpreted in terms of the volume of the moduli space of flat connections on certain Riemann surfaces. More precisely, it is equal to the Rényi entropy of certain states prepared in topological 2 d Yang-Mills theory with SU(2) gauge group. Using the analytic techniques, we show that the universal part comprises of Riemann zeta functions and can be written in terms of the partition functions of two-dimensional topological Yang-Mills theory. We further propose that the large k limiting value of the Rényi entropy of torus links of type T p,pn is the sum of two parts: (i) the universal part which is independent of n, and (ii) the non-universal or the linking part which explicitly depends on the linking number n. We present a detailed analysis of several torus links and observe that the entropies converge to a finite value in the semiclassical limit. The focal point of this work is the asymptotic behavior of the Rényi entropies, including the entanglement entropy, in the semiclassical limit of k → ∞. We study the multi-boundary entanglement structure of the state associated with the torus link complement S 3 \T p,q in the set-up of three-dimensional SU(2) k Chern-Simons theory.
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