The Fusion Categorical Diagonal
Daniel Robbins, Thomas Vandermeulen

TL;DR
This paper introduces a Frobenius algebra in fusion categories to generalize the diagonal subgroup, enabling the extension of field theories to non-invertible symmetries and providing explicit calculations for theories with symmetric group-based symmetries.
Contribution
It defines a new Frobenius algebra structure over fusion categories that generalizes the diagonal subgroup, extending field theoretical constructions to non-invertible symmetries.
Findings
Explicit calculations for theories with Rep(S_3)×Rep(S_3) symmetry.
Application of the algebra to gauging topological quantum field theories.
Discussion on Morita equivalence in symmetry categories.
Abstract
We define a Frobenius algebra over fusion categories of the form RepRep which generalizes the diagonal subgroup of . 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 RepRep 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Black Holes and Theoretical Physics
