Published June 15, 2021
| Submitted + Published
Journal Article
Open
ℤ_N symmetries, anomalies, and the modular bootstrap
- Creators
-
Lin, Ying-Hsuan
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Shao, Shu-Heng
Abstract
We explore constraints on (1+1)d unitary conformal field theory with an internal ℤ_N global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the modular bootstrap. Among the other constraints we have found, we prove the existence of a ℤ_N-symmetric relevant/marginal operator if N−1 ≤ c ≤ 9−N for N ≤ 4, with the end points saturated by various Wess-Zumino-Witten models that can be embedded into (e₈)₁. Its existence implies that robust gapless fixed points are not possible in this range of c if only a ℤ_N symmetry is imposed microscopically. We also obtain stronger, more refined bounds that depend on the 't Hooft anomaly of the ℤ_N symmetry.
Additional Information
© 2021 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3. Received 3 February 2021; accepted 29 April 2021; published 1 June 2021. We thank Luca Delacrétaz, Meng Cheng, Pranay Gorantla, Theo Johnson-Freyd, Zohar Komargodski, Ho Tat Lam, Michael Levin, Kantaro Ohmori, and Nathan Seiberg for helpful discussions. We are grateful to Meng Cheng, Theo Johnson-Freyd, and Justin Kulp for comments on the first draft. Y. L. is supported by the Sherman Fairchild Foundation, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the Simons Collaboration Grant on the Nonperturbative Bootstrap. S. H. S. is supported by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440, NS). This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958.Attached Files
Published - PhysRevD.103.125001.pdf
Submitted - 2101.08343.pdf
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2101.08343.pdf
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Additional details
- Alternative title
- ZN symmetries, anomalies, and the modular bootstrap
- Eprint ID
- 107651
- Resolver ID
- CaltechAUTHORS:20210122-075637022
- Sherman Fairchild Foundation
- DE-SC0011632
- Department of Energy (DOE)
- 651440
- Simons Foundation
- PHY-1748958
- NSF
- SCOAP3
- Created
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2021-01-22Created from EPrint's datestamp field
- Updated
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2021-06-01Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2021-002