Physics#Conformal Field Theory, Topological Quantum Field Theory, Duality🔬 ResearchAnalyzed: Jan 3, 2026 16:43
Generalized Level-Rank Duality and Non-Invertible Anyon Condensation in CFT
Published:Dec 30, 2025 19:00
•1 min read
•ArXiv
Analysis
This paper explores the connections between holomorphic conformal field theory (CFT) and dualities in 3D topological quantum field theories (TQFTs), extending the concept of level-rank duality. It proposes that holomorphic CFTs with Kac-Moody subalgebras can define topological interfaces between Chern-Simons gauge theories. Condensing specific anyons on these interfaces leads to dualities between TQFTs. The work focuses on the c=24 holomorphic theories classified by Schellekens, uncovering new dualities, some involving non-abelian anyons and non-invertible symmetries. The findings generalize beyond c=24, including a duality between Spin(n^2)_2 and a twisted dihedral group gauge theory. The paper also identifies a sequence of holomorphic CFTs at c=2(k-1) with Spin(k)_2 fusion category symmetry.
Key Takeaways
- •Explores connections between holomorphic CFT and dualities in 3D TQFTs.
- •Proposes a mechanism for generating dualities via anyon condensation on topological interfaces.
- •Identifies new dualities, including those involving non-abelian anyons and non-invertible symmetries.
- •Generalizes findings beyond c=24, providing examples like Spin(n^2)_2 duality.
- •Deduces the existence of holomorphic CFTs with Spin(k)_2 fusion category symmetry.
Reference
“The paper discovers novel sporadic dualities, some of which involve condensation of anyons with non-abelian statistics, i.e. gauging non-invertible one-form global symmetries.”