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Anomalies and Bounds on Charged Operators

Lin, Ying-Hsuan and Shao, Shu-Heng (2019) Anomalies and Bounds on Charged Operators. Physical Review D, 100 (2). Art. No. 025013. ISSN 2470-0010. http://resolver.caltech.edu/CaltechAUTHORS:20190709-150923766

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Abstract

We study the implications of the ’t Hooft anomaly (i.e., obstruction to gauging) on conformal field theory, focusing on the case when the global symmetry is Z_2. Using the modular bootstrap, universal bounds on (1+1)-dimensional bosonic conformal field theories with an internal Z_2 global symmetry are derived. The bootstrap bounds depend dramatically on the ’t Hooft anomaly. In particular, there is a universal upper bound on the lightest Z_2 odd operator if the symmetry is anomalous, but there is no bound if the symmetry is nonanomalous. In the nonanomalous case, we find that the lightest Z_2 odd state and the defect ground state cannot both be arbitrarily heavy. We also consider theories with a U(1) global symmetry, and comment that there is no bound on the lightest U(1) charged operator if the symmetry is nonanomalous.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.100.025013DOIArticle
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.100.025013PublisherArticle
https://arxiv.org/abs/1904.04833arXivDiscussion Paper
ORCID:
AuthorORCID
Lin, Ying-Hsuan0000-0001-8904-1287
Shao, Shu-Heng0000-0003-1294-2786
Additional Information:© 2019 Published by the American Physical Society. 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 23 April 2019; published 25 July 2019. We thank N. Arkani-Hamed, N. Benjamin, C. Cordova, P.-S. Hsin, Z. Komargodski, M. Levin, K. Ohmori, P. Putrov, T. Rudelius, N. Seiberg, D Simmons-Duffin, J. Wang, and E. Witten for interesting discussions. Y. L. 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 No. DE-SC0011632. The work of S. H. S. is supported by the National Science Foundation Grant No. PHY-1606531 and by the Roger Dashen Membership.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
NSFPHY-1606531
Roger Dashen MembershipUNSPECIFIED
SCOAP3UNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2019-009
Issue or Number:2
Record Number:CaltechAUTHORS:20190709-150923766
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190709-150923766
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97007
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:09 Jul 2019 22:44
Last Modified:25 Jul 2019 16:28

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