Entanglement on multiple S2 boundaries in Chern-Simons theory

  • Siddharth DwivediEmail author
  • Vivek Kumar Singh
  • P. Ramadevi
  • Yang Zhou
  • Saswati Dhara
Open Access
Regular Article - Theoretical Physics


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 S2 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 S2. 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 S2 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.


Chern-Simons Theories Conformal Field Theory Topological Field Theories Wilson ’t Hooft and Polyakov loops 


Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Center for Theoretical Physics, College of Physical Science and TechnologySichuan UniversityChengduChina
  2. 2.Faculty of PhysicsUniversity of WarsawWarsawPoland
  3. 3.Department of PhysicsIndian Institute of Technology BombayMumbaiIndia
  4. 4.Department of Physics and Center for Field Theory and Particle PhysicsFudan UniversityShanghaiChina

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