Journal of High Energy Physics (Aug 2019)
Entanglement on multiple S 2 boundaries in Chern-Simons theory
Abstract
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.
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