Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes

2025/05/01 by Mertens, Thomas G., Wu, Qi-Feng
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2505.00501

Abstract

One approach to analyzing entanglement in a gauge theory is embedding it into a factorized theory with edge modes on the entangling boundary. For topological quantum field theories (TQFT), this naturally leads to factorizing a TQFT by adding local edge modes associated with the corresponding CFT. In this work, we instead construct a minimal set of edge modes compatible with the topological invariance of Chern-Simons theory. This leads us to propose a minimal factorization map. These minimal edge modes can be interpreted as the degrees of freedom of a particle on a quantum group. Of particular interest is three-dimensional gravity as a Chern-Simons theory with gauge group SL(2,ℝ) × SL(2,ℝ). Our minimal factorization proposal uniquely gives rise to quantum group edge modes factorizing the bulk state space of 3d gravity. This agrees with earlier proposals that relate the Bekenstein-Hawking entropy in 3d gravity to topological entanglement entropy.

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• Entanglement entropy and edge modes in topological string theory: I
• Topological Quantum Field Theories -- A Meeting Ground for Physicists and Mathematicians
• Topological Quantum Field Theories from Compact Lie Groups
• Topological Preparation of Non-Stabilizer States and Clifford Evolution in SU(2)₁ Chern-Simons Theory