Entanglement on multiple $S^2$ boundaries in Chern-Simons theory

Abstract

Topological entanglement structure amongst disjoint torus boundaries of three manifolds have already been studied within the context of Chern-Simons theory. In this work, we study the topological entanglement due to interaction between the quasiparticles inside three-manifolds with one or more disjoint $S^2$ boundaries in SU($N$) Chern-Simons theory. We focus on the world-lines of quasiparticles (Wilson lines), carrying SU($N$) representations, creating four punctures on every $S^2$. We compute the entanglement entropy by partial tracing some of the boundaries. In fact, the entanglement entropy depends on the SU($N$) representations on these four-punctured $S^2$ boundaries. Further, we observe interesting features on the GHZ-like and W-like entanglement structures. Such a distinction crucially depends on the multiplicity of the irreducible representations in the tensor product of SU($N$) representations.

arXiv comment62 pages, 20 figures. Four new references added. Matches with published version

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Cited by in corpus (8)

• Distinguishing Mutant Knots
• Entanglement Classification from a Topological Perspective
• Semiclassical limit of topological Rényi entropy in $3d$ Chern-Simons theory
• Multi-boundary entanglement in Chern-Simons theory with finite gauge groups
• Topological entanglement and hyperbolic volume
• Level-rank duality of knot and link invariants
• Topological entanglement entropy for torus knot bipartitions and the Verlinde-like formulas
• Topological entanglement and number theory