TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.6.154
TI  - Von Neumann subfactors and non-invertible symmetries
PY  - 2025/12/15
UR  - https://scipost.org/SciPostPhys.19.6.154
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 6
SP  - 154
A1  - Yu, Xingyang
AU  - Zhang, Hao Y.
AB  - We use the language of von Neumann subfactors to investigate non-invertible symmetries in two dimensions. A fusion categorical symmetry $\mathcal{C}$, its module category $\mathcal{M}$, and a gauging labeled by an algebra object $\mathcal{A}$ are encoded in the bipartite principal graph of a subfactor. The dual principal graph captures the quantum symmetry $\mathcal{C}'$ obtained by gauging $\mathcal{A}$ in $\mathcal{C}$, as well as a reverse gauging back to $\mathcal{C}$. From a given subfactor $N \subset M$, we derive a quiver diagram that encodes the representations of the associated non-invertible symmetry. We show how this framework provides necessary conditions for admissible gaugings, enabling the construction of generalized orbifold groupoids. To illustrate this strategy, we present three examples: Rep$(D_4)$ as a warm-up, the higher-multiplicity case Rep$(A_4)$ with its associated generalized orbifold groupoid and triality symmetry, and Rep$(A_5)$, where $A_5$ is the smallest non-solvable finite group. For applications to gapless systems, we embed these generalized gaugings as global manipulations on the conformal manifolds of $c=1$ CFTs and uncover new self-dualities in the exceptional $SU(2)_1/A_5$ theory. For $\mathcal{C}$-symmetric TQFTs, we use the subfactor-derived quiver diagrams to characterize gapped phases, describe their vacuum structure, and classify the recently proposed particle-soliton degeneracies.
ER  -

@Article{10.21468/SciPostPhys.19.6.154,
	title={{Von Neumann subfactors and non-invertible symmetries}},
	author={Xingyang Yu and Hao Y. Zhang},
	journal={SciPost Phys.},
	volume={19},
	pages={154},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.6.154},
	url={https://scipost.org/10.21468/SciPostPhys.19.6.154},
}