Generalized level-rank duality, holomorphic conformal field theory, and non-invertible anyon condensation

A bstract We study the interplay between holomorphic conformal field theory and dualities of 3D topological quantum field theories generalizing the paradigm of level-rank duality. A holomorphic conformal field theory with a Kac-Moody subalgebra implies a topological interface between Chern-Simons gauge theories. Upon condensing a suitable set of anyons, such an interface yields a duality between topological field theories. We illustrate this idea using the c = 24 holomorphic theories classified by Schellekens, which leads to a list of novel sporadic dualities. Some of these dualities necessarily involve condensation of anyons with non-abelian statistics, i.e. gauging non-invertible one-form global symmetries. Several of the examples we discover generalize from c = 24 to an infinite series. This includes the fact that Spin( n 2 ) 2 is dual to a twisted dihedral group gauge theory. Finally, if –1 is a quadratic residue modulo k , we deduce the existence of a sequence of holomorphic CFTs at central charge c = 2( k − 1) with fusion category symmetry given by Spin( k ) 2 or equivalently, the ℤ 2 -equivariantization of a Tambara-Yamagami fusion category.