A newly constructed McDuff II1 factor contains a braided fusion category that is surprisingly not modular.
April 25, 2026
Original Paper
Gauging the Categorical Connes' $\tilde\chi(M)$
arXiv · 2604.21833
The Takeaway
Mathematical theory previously lacked a physical example of this specific type of operator algebra. The construction proves that non-modular braided fusion categories exist within this framework. This discovery fills a major gap in the study of quantum invariants and von Neumann algebras. It provides a concrete subject for physicists studying topological phases of matter. Researchers can now use this model to explore new behaviors in quantum information theory.
From the abstract
We prove that if a finite group $G$ acts outerly on a McDuff $\rm II_1$ factor $M$, then $\mathsf{Rep}(G/KL)$ is a braided monoidal full subcategory of the categorical Connes' $\tilde{\chi}(M\rtimes G)$ defined inarXiv:2111.06378, where $K$ and $L$ are the centrally trivial and approximately inner parts in $G$ respectively.When $L$ is trivial, we give an explicit formula for the $G/K$-gauging procedure on $\tilde{\chi}(M\rtimes G)$. This is the categorical generalization of Connes' short exact s