Non-invertible anyon condensation and level-rank dualities
- 1University of Chicago
Abstract
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})/\mathcal{A}_{N}, ( 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})/\mathcal{B}_{N} ( 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})/\mathcal{C}_{N} ( U S p ( 2 N ) 1 × S O ( N ) − 4 ) / 𝒞 N arising from conformal embeddings, where \mathcal{A}_{N}, \mathcal{B}_{N}, 𝒜 N , ℬ N , and \mathcal{C}_{N} 𝒞 N are appropriate collections of gauged non-invertible bosons.
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BibTeX
@article{cordova2026noninvertible,
title = {{Non-invertible anyon condensation and level-rank dualities}},
author = {Clay Córdova and Diego García-Sepúlveda},
journal = {SciPost Physics},
year = {2026},
month = oct,
doi = {10.21468/scipostphys.21.4.089},
url = {https://scipost.org/10.21468/SciPostPhys.21.4.089},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Non-invertible anyon condensation and level-rank dualities
AU - Clay Córdova
AU - Diego García-Sepúlveda
PY - 2026
DA - 2026/10/09
JO - SciPost Physics
DO - 10.21468/scipostphys.21.4.089
UR - https://scipost.org/10.21468/SciPostPhys.21.4.089
AB - 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})/\mathcal{A}_{N}, ( 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})/\mathcal{B}_{N} ( 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})/\mathcal{C}_{N} ( U S p ( 2 N ) 1 × S O ( N ) − 4 ) / 𝒞 N arising from conformal embeddings, where \mathcal{A}_{N}, \mathcal{B}_{N}, 𝒜 N , ℬ N , and \mathcal{C}_{N} 𝒞 N are appropriate collections of gauged non-invertible bosons.
SN - 2542-4653
ER -