Topological defect lines and renormalization group flows in two dimensions

By Chi-Ming Chang, Ying-Hsuan Lin, Shu-Heng Shao, Yifan Wang, Xi Yin. Journal of High Energy Physics, 2018

357 citations recorded by the source corpus.

A bstractWe consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the ’t Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.

Subfields: Condensed Matter Physics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d88ca8dfd98a6a2c2fb09561ac34ddf7d3353903

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Citations in the corpus

Higher Gauging and Non-invertible Condensation Defects (2022, background): “, for the 1-form symmetry to be 1-gaugeable, we demand the crossing of the lines, which is captured by the F -symbols, to be trivial (see [97,3,4,93,17] for discussions on the obstruction to gauging in 1+1d).”
Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions (2022, background): “Building on earlier work of [2–7], it has been advocated that non-invertible topological defects should be viewed as generalizations of ordinary global symmetries [8, 9].”
Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, background): “We expect this defect to be topological [135–137].”
Universal Non‐Invertible Symmetries (2022, unknown): “We refer the readers to the textbook [27] for a more careful exposition and [37, 38] for physicists-friendly reviews.”
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond (2022, methodology): “In particular, using a modular invariance argument, it was shown in [91] (see also [97] for generalizations) that the existence of certain non-invertible topological lines is incompatible with a trivially gapped phase.”
On 2-group global symmetries and their anomalies (2018, unknown): “Recent investigations include [2, 3].”
Generalized Symmetries in Condensed Matter (2022, unknown): “In a theory with such a symmetry operator, RG flows generated by a perturbation by a local operator can only generate operators that pass freely through the wall (96, 101).”
Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases (2019, methodology): “This captures the anomalies discussed in [9].”