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Bounds on 4D conformal and superconformal field theories

Poland, David and Simmons-Duffin, David (2011) Bounds on 4D conformal and superconformal field theories. Journal of High Energy Physics, 2011 (5). Art. No. 017. ISSN 1029-8479. https://resolver.caltech.edu/CaltechAUTHORS:20170816-080350311

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Abstract

We derive general bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N = 1 superconformal field theories. In any CFT containing a scalar primary ϕ of dimension d we show that crossing symmetry of ⟨ϕϕϕϕ⟩ implies a completely general lower bound on the central charge c ≥ f_c(d). Similarly, in CFTs containing a complex scalar charged under global symmetries, we bound a combination of symmetry current two-point function coefficients τ^(IJ) and flavor charges. We extend these bounds to N = 1 superconformal theories by deriving the superconformal block expansions for four-point functions of a chiral superfield Φ and its conjugate. In this case we derive bounds on the OPE coefficients of scalar operators appearing in the Φ × Φ^† OPE, and show that there is an upper bound on the dimension of Φ^†Φ when dim Φ is close to 1. We also present even more stringent bounds on c and τ^(IJ). In supersymmetric gauge theories believed to flow to superconformal fixed points one can use anomaly matching to explicitly check whether these bounds are satisfied.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/JHEP05(2011)017DOIArticle
https://link.springer.com/article/10.1007/JHEP05%282011%29017#Abs1PublisherArticle
https://arxiv.org/abs/1009.2087arXivDiscussion Paper
ORCID:
AuthorORCID
Poland, David0000-0003-3854-2430
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2011 SISSA, Trieste, Italy. Received: April 4, 2011 Accepted: April 15, 2011 Published: May 3, 2011 We thank Tom Hartman, Diego Hofman, and especially Clay Córdova for helpful comments and conversations. DP also thanks the Aspen Center for Physics for its hospitality during the completion of this work. This work is supported in part by the Harvard Center for the Fundamental Laws of Nature and by NSF grant PHY-0556111.
Funders:
Funding AgencyGrant Number
Harvard Center for the Fundamental Laws of NatureUNSPECIFIED
NSFPHY-0556111
Subject Keywords:Supersymmetric gauge theory Conformal and W Symmetry
Issue or Number:5
Record Number:CaltechAUTHORS:20170816-080350311
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170816-080350311
Official Citation:Poland, D. & Simmons-Duffin, D. J. High Energ. Phys. (2011) 2011: 17. https://doi.org/10.1007/JHEP05(2011)017
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80461
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:16 Aug 2017 22:52
Last Modified:03 Oct 2019 18:31

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