Topological defect lines and renormalization group flows in two dimensions

  • Chi-Ming Chang
  • Ying-Hsuan Lin
  • Shu-Heng ShaoEmail author
  • Yifan Wang
  • Xi Yin
Open Access
Regular Article - Theoretical Physics


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.


Anomalies in Field and String Theories Conformal Field Theory Global Symmetries 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Chi-Ming Chang
    • 1
  • Ying-Hsuan Lin
    • 2
  • Shu-Heng Shao
    • 3
    Email author
  • Yifan Wang
    • 4
  • Xi Yin
    • 5
  1. 1.Center for Quantum Mathematics and Physics (QMAP)University of CaliforniaDavisU.S.A.
  2. 2.Walter Burke Institute for Theoretical Physics, California Institute of TechnologyPasadenaU.S.A.
  3. 3.School of Natural Sciences, Institute for Advanced StudyPrincetonU.S.A.
  4. 4.Joseph Henry LaboratoriesPrinceton UniversityPrincetonU.S.A.
  5. 5.Jefferson Physical LaboratoryHarvard UniversityCambridgeU.S.A.

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