Semiclassical limit of topological Rényi entropy in 3d Chern-Simons theory

A bstract 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. The focal point of this work is the asymptotic behavior of the Rényi entropies, including the entanglement en...

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Vydáno v:	The journal of high energy physics Ročník 2020; číslo 12; s. 1 - 72
Hlavní autoři:	Dwivedi, Siddharth, Singh, Vivek Kumar, Roy, Abhishek
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2020 Springer Nature B.V SpringerOpen
Témata:	Asymptotic properties Chern-Simons Theories Classical and Quantum Gravitation Conformal Field Theory Convergence Elementary Particles Entropy Field theory (physics) High energy physics Hilbert space Links Partitions (mathematics) Physics Physics and Astronomy Quantum entanglement Quantum Field Theories Quantum Field Theory Quantum Physics Quantum theory Regular Article - Theoretical Physics Relativity Theory Riemann surfaces Spacetime String Theory Topological Field Theories Topology Toruses Wilson ’t Hooft and Polyakov loops Yang-Mills theory Topological Field Theories Wilson ’t Hooft and Polyakov loops Chern-Simons Theories Conformal Field Theory
ISSN:	1029-8479, 1029-8479
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Shrnutí:	A bstract 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. 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 present a detailed analysis of several torus links and observe that the entropies converge to a finite value in the semiclassical limit. 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 . 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. 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. 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. 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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1029-8479 1029-8479
DOI:	10.1007/JHEP12(2020)132