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. https://resolver.caltech.edu/CaltechAUTHORS:20210122-075637022

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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.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1103/PhysRevD.103.125001	DOI	Article
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.103.125001	Publisher	Article
https://arxiv.org/abs/2101.08343	arXiv	Discussion Paper

ORCID:

Author	ORCID
Lin, Ying-Hsuan	0000-0001-8904-1287
Shao, Shu-Heng	0000-0003-1294-2786

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

Funders:

Funding Agency	Grant Number
Sherman Fairchild Foundation	UNSPECIFIED
Department of Energy (DOE)	DE-SC0011632
Simons Foundation	651440
NSF	PHY-1748958
SCOAP3	UNSPECIFIED

Other Numbering System:

Other Numbering System Name	Other Numbering System ID
CALT-TH	2021-002

Issue or Number:

DOI:

10.1103/PhysRevD.103.125001

Record Number:

CaltechAUTHORS:20210122-075637022

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20210122-075637022

Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

107651

Collection:

CaltechAUTHORS

Deposited By:

Joy Painter

Deposited On:

22 Jan 2021 18:25

Last Modified:

01 Jun 2021 19:52

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