Non-invertible Symmetries via Subfactors: Conformal and Topological Applications

Abstract: Non-invertible symmetries, characterized by fusion categories rather than groups, play a central role in modern quantum field theory and topological phases of matter. In this talk, I will introduce a von Neumann subfactor approach to non-invertible symmetries in two dimensions. Subfactors encode fusion categorical data—including symmetries, module categories, and dual symmetries—via their bipartite principal graphs. I will explain how these structures naturally encode generalized gaugings and dualities, and illustrate their physical implications in both conformal and topological settings. In particular, I will discuss new self-dualities in $c=1$ CFTs, such as the exceptional orbifold $SU(2)_1/A_5$, and present a classification of particle-soliton degeneracies in gapped phases with various non-invertible symmetries. This framework provides a concrete computational toolkit that bridges subfactor theory and physical non-invertible symmetries.

condensed mattergeneral relativity and quantum cosmologyHEP - latticeHEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

Quantum Theories of Fields, Matter, and Strings

Series comments: A series of talks covering a broad range of topics in theoretical physics, including high energy theory, condensed matter, and string theory.

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