Entanglement entropies in 2d holographic CFTs are rewritten via crossing symmetry as algebraic Virasoro entropies whose O(c) piece is identified with the RT area through saddle-dominated Cardy density after coarse-graining heavy primaries into Liouville-momentum bins.
Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes
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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$(2,\mathbb{R}) \times$ SL$(2,\mathbb{R})$. 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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hep-th 1years
2026 1verdicts
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Ryu-Takayanagi area from Virasoro modular data
Entanglement entropies in 2d holographic CFTs are rewritten via crossing symmetry as algebraic Virasoro entropies whose O(c) piece is identified with the RT area through saddle-dominated Cardy density after coarse-graining heavy primaries into Liouville-momentum bins.