Kavli Affiliate: Jeffrey Harvey
| Summary:
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 $mathrmSpin(k)_2$ or equivalently, the $mathbbZ_2$-equivariantization of a Tambara-Yamagami fusion category.
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