Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases

By Ryan Thorngren, Yifan Wang. 2019

190 citations recorded by the source corpus.

We study generalized discrete symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. In particular, we describe 't Hooft anomalies and classify gapped phases stabilized by these symmetries, including new 1+1D topological phases. The algebra of these operators is not a group but rather is described by their fusion ring and crossing relations, captured algebraically as a fusion category. Such data defines a Turaev-Viro/Levin-Wen model in 2+1D, while a 1+1D system with this fusion category acting as a global symmetry defines a boundary condition. This is akin to gauging a discrete global symmetry at the boundary of Dijkgraaf-Witten theory. We describe how to "ungauge" the fusion category symmetry in these boundary conditions and separate the symmetry-preserving phases from the symmetry-breaking ones. For Tambara-Yamagami categories and their generalizations, which are associated with Kramers-Wannier-like self-dualities under orbifolding, we develop gauge theoretic techniques which simplify the analysis. We include some examples of CFTs with fusion category symmetry derived from Kramers-Wannier-like dualities as an appetizer for the Part II companion paper.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b6837cf0f3016fbbb2876880e936cbf49665fbd6

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Citations in the corpus

Topological Defects on the Lattice: Dualities and Degeneracies (2020, unknown): “A partial list includes [126, 127, 128, 129, 130, 131, 132, 133, 134].”
Generalized Symmetries in Condensed Matter (2022, unknown): “(100, 106) argue that a 1+1d system with fusion category symmetry can always be realized as a boundary condition of a gapped 2+1 dimensional topological order with anyon types carrying the associated labels of the topological operators.”
Orbifold groupoids (2020, background): “The Z2 symmetry is interesting and is well discussed in a number of recent papers, for example [32, 33, 64] as well as most classic references on CFT.”
Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions (2022, background): “(See [20, 21] for a physical perspective on 1+1d defects analogous to that presented here.”
Higher Gauging and Non-invertible Condensation Defects (2022, background): “These anomalies lead to non-trivial dynamical constraints on the renormalization group flows [4,15,18,36,46], generalizing the conventional ’t Hooft anomaly matching argument.”