Topological Defect Lines and Renormalization Group Flows in Two Dimensions
Abstract
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.
Additional Information
© 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: July 12, 2018; Revised: December 11, 2018; Accepted: December 23, 2018; Published: January 3, 2019. We would like to thank Philip Argyres, Nathan Benjamin, Lakshya Bhardwaj, Aleksey Cherman, Minjae Cho, Scott Collier, Clay Cordova, Thomas Dumitrescu, Davide Gaiotto, Zohar Komargodski, Liang Kong, Kantaro Ohmori, Hirosi Ooguri, Nathan Seiberg, David Simmons-Duffin, Yuji Tachikawa, Cumrun Vafa, Juven Wang, Edward Witten, and Cenke Xu for discussions. We also thank Minjae Cho, Scott Collier, Liang Kong, and Yuji Tachikawa for comments on a preliminary draft. This project was initiated at the working group 2D Conformal and Modular Bootstrap at the Aspen Center for Physics. CC thanks California Institute of Technology, Yau Mathematical Sciences Center at Tsinghua University, XY thanks Boston University, Rutgers University, Mitchell Institute at Texas A&M University, CC and YW thank Superconformal Field Theories in 6 and Lower Dimensions Workshop at Tsinghua Sanya International Mathematics Forum, YW and XY thank the annual meeting of the Simons Collaboration on Non-Perturbative Bootstrap, for their hospitality during the course of this work. CC is supported in part by the U.S. Department of Energy grant DE-SC0009999. YL is supported by the Sherman Fairchild Foundation, and by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. SHS is supported by the Zurich Insurance Company Membership and the National Science Foundation grant PHY-1314311. YW is supported in part by the US NSF under Grant No. PHY-1620059 and by the Simons Foundation Grant No. 488653. XY is supported by a Simons Investigator Award from the Simons Foundation and by DOE grant DE-FG02-91ER40654.Attached Files
Published - Chang2019_Article_TopologicalDefectLinesAndRenor.pdf
Submitted - 1802.04445.pdf
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Additional details
- Eprint ID
- 84995
- Resolver ID
- CaltechAUTHORS:20180228-093901341
- DE-SC0009999
- Department of Energy (DOE)
- Sherman Fairchild Foundation
- DE-SC0011632
- Department of Energy (DOE)
- Zurich Insurance Company
- PHY-1314311
- NSF
- PHY-1620059
- NSF
- 488653
- Simons Foundation
- DE-FG02-91ER40654
- Department of Energy (DOE)
- SCOAP3
- Created
-
2018-02-28Created from EPrint's datestamp field
- Updated
-
2021-11-15Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2017-067