2017
DOI: 10.1007/jhep04(2017)061
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Multi-boundary entanglement in Chern-Simons theory and link invariants

Abstract: We consider Chern-Simons theory for gauge group G at level k on 3-manifolds M n with boundary consisting of n topologically linked tori. The Euclidean path integral on M n defines a quantum state on the boundary, in the n-fold tensor product of the torus Hilbert space. We focus on the case where M n is the link-complement of some n-component link inside the threesphere S 3 . The entanglement entropies of the resulting states define framing-independent link invariants which are sensitive to the topology of the … Show more

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Cited by 49 publications
(111 citation statements)
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“…. ∪ T 2 ) was initiated in [13,14]. The quantum states in these works are obtained by performing the path integral of Chern-Simons theory on link complements with n torus boundaries.…”
Section: Contentsmentioning
confidence: 99%
“…. ∪ T 2 ) was initiated in [13,14]. The quantum states in these works are obtained by performing the path integral of Chern-Simons theory on link complements with n torus boundaries.…”
Section: Contentsmentioning
confidence: 99%
“…(B.1)) being a generator of modular group SL(2, Z) of torus diffeomorphism. With this link state, the reduced density matrix elements corresponding to a bi-partition (1|1) can be computed (see for example [25]):…”
Section: Example-1: Rényi Entropy For Hopf Link State For Generic Groupmentioning
confidence: 99%
“…The Hopf link is a member of this family with n = 1. Using the results of [25], the Rényi entropy of T (2, 2n) link state can be given for U(1) group as following:…”
Section: Rényi Divergence D α (L H)mentioning
confidence: 99%
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