Topological defect lines and renormalization group flows in two dimensions

Chang, Chi-Ming; Lin, Ying-Hsuan; Shao, Shu-Heng; Wang, Yifan; Yin, Xi

doi:10.1007/JHEP01(2019)026

Title: Topological defect lines and renormalization group flows in two dimensions

Journal Article · 03 January 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP01(2019)026 · OSTI ID:1597494

Chang, Chi-Ming ^[1]; Lin, Ying-Hsuan ^[2]; Shao, Shu-Heng ^[3]; Wang, Yifan ^[4]; Yin, Xi ^[5]

Univ. of California, Davis, CA (United States); Caltech
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Princeton Univ., NJ (United States). Joseph Henry Lab. of Physics
Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.

We 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.

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Research Organization:: California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of California, Davis, CA (United States); Harvard Univ., Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0011632; SC0009999; SC0007870; FG02-91ER40654

OSTI ID:: 1597494

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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