Non-invertible anyon condensation and level-rank dualities

We derive new dualities of topological quantum field theories in three spacetime dimensions that generalize the familiar level-rank dualities of Chern-Simons gauge theories. The key ingredient in these dualities is non-Abelian anyon condensation, which is a gauging operation for topological lines with non-group-like i.e. non-invertible fusion rules. We find that, generically, dualities involve such non-invertible anyon condensation and that this unifies a variety of exceptional phenomena in topological field theories and their associated boundary rational conformal field theories, including conformal embeddings, and Maverick cosets (those where standard algorithms for constructing a coset model fail.) We illustrate our discussion in a variety of isolated examples as well as new infinite series of dualities involving non-Abelian anyon condensation including: i) a new description of the parafermion theory as (SU(N)₂ × Spin(N)₋₄)/AN, ( S U ( N ) 2 × S p i n ( N ) − 4 ) / 𝒜 N , ii) a new presentation of a series of points on the orbifold branch of c=1 c = 1 conformal field theories as (Spin(2N)₂ × Spin(N)₋₂ × Spin(N)₋₂)/BN ( S p i n ( 2 N ) 2 × S p i n ( N ) − 2 × S p i n ( N ) − 2 ) / ℬ N , and iii) a new dual form of SU(2)N S U ( 2 ) N as (USp(2N)₁ × SO(N)₋₄)/CN ( U S p ( 2 N ) 1 × S O ( N ) − 4 ) / 𝒞 N arising from conformal embeddings, where AN, BN,