2024/05/13 by Daniel Robbins, Robbins, Daniel, Thomas Vandermeulen +1
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics
paper · pdf · doi:10.48550/arxiv.2405.08058
We define a Frobenius algebra over fusion categories of the form Rep(G)\boxtimesRep(G) which generalizes the diagonal subgroup of G× G. This allows us to extend field theoretical constructions which depend on the existence of a diagonal subgroup to non-invertible symmetries. We give explicit calculations for theories with Rep(S3)\boxtimesRep(S3) symmetry, applying the results to gauging topological quantum field theories which carry this non-invertible symmetry. Along the way, we also discuss how Morita equivalence is implemented for algebras in symmetry categories.