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ℤ_N symmetries, anomalies, and the modular bootstrap

Lin, Ying-Hsuan and Shao, Shu-Heng (2021) ℤ_N symmetries, anomalies, and the modular bootstrap. Physical Review D, 103 (12). Art. No. 125001. ISSN 2470-0010. doi:10.1103/PhysRevD.103.125001.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Lin, Ying-Hsuan0000-0001-8904-1287
Shao, Shu-Heng0000-0003-1294-2786
Alternate Title:ZN symmetries, anomalies, and the modular bootstrap
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.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Simons Foundation651440
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Issue or Number:12
Record Number:CaltechAUTHORS:20210122-075637022
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107651
Deposited By: Joy Painter
Deposited On:22 Jan 2021 18:25
Last Modified:01 Jun 2021 19:52

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