Entanglement on multiple $S^2$ boundaries in Chern-Simons theory
arXiv:1906.11489 · doi:10.1007/JHEP08(2019)034
The paper investigates topological entanglement in SU(N) Chern‑Simons theory for three‑manifolds with one or more disjoint S² boundaries, analyzing how Wilson lines and their representations affect the entanglement entropy and revealing GHZ‑like and W‑like entanglement patterns.
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.
62 pages, 20 figures. Four new references added. Matches with published version