Minimal factorization of Chern-Simons theory – Gravitational anyonic edge modes, by Thomas G. Mertens, Qi-Feng Wu

SciPost Physics Home Authoring Refereeing Submit a manuscript About Minimal factorization of Chern-Simons theory – Gravitational anyonic edge modes Thomas G. Mertens, Qi-Feng Wu SciPost Phys. 20, 095 (2026) · published 1 April 2026 doi: 10.21468/SciPostPhys.20.4.095 pdf BiBTeX RIS Submissions/Reports 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$(2,\mathbb{R}) ×$ 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. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.4.095TI - Minimal factorization of Chern-Simons theory – Gravitational anyonic edge modesPY - 2026/04/01UR - https://scipost.org/SciPostPhys.20.4.095JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 4SP - 095A1 - Mertens, Thomas G.AU - Wu, Qi-FengAB - 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$(2,\mathbb{R}) ×$ 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.ER - × @Article{10.21468/SciPostPhys.20.4.095, title={{Minimal factorization of Chern-Simons theory – Gravitational anyonic edge modes}}, author={Thomas G. Mertens and Qi-Feng Wu}, journal={SciPost Phys.}, volume={20}, pages={095}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.4.095}, url={https://scipost.org/10.21468/SciPostPhys.20.4.095},} Ontology / Topics See full Ontology or Topics database. AdS$_3$ gravity Chern-Simons theory Entanglement Authors / Affiliation: mappings to Contributors and Organizations See all Organizations. 1 Thomas G. Mertens, 1 Qi-Feng Wu 1 Universiteit Gent / Ghent University Funder for the research work leading to this publication European Research Council [ERC]