Generalized Level-Rank Duality and Non-Invertible Anyon Condensation in CFT
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.
“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.”