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Carving out the space of 4D CFTs

Poland, David and Simmons-Duffin, David and Vichi, Alessandro (2012) Carving out the space of 4D CFTs. Journal of High Energy Physics, 2012 (5). Art. No. 110. ISSN 1029-8479. doi:10.1007/JHEP05(2012)110.

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We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N = 1 superconformal field theories. Using our algorithm, we dramatically improve previous bounds on a number of CFT quantities, particularly for theories with global symmetries. In the case of SO(4) or SU(2) symmetry, our bounds severely constrain models of conformal technicolor. In N = 1 superconformal theories, we place strong bounds on dim(Φ^†Φ), where Φ is a chiral operator. These bounds asymptote to the line dim(Φ^†Φ) ≤ 2 dim(Φ) near dim(Φ) ≃ 1, forbidding positive anomalous dimensions in this region. We also place novel upper and lower bounds on OPE coefficients of protected operators in the Φ × Φ OPE. Finally, we find examples of lower bounds on central charges and flavor current two-point functions that scale with the size of global symmetry representations. In the case of N = 1 theories with an SU(N) flavor symmetry, our bounds on current two-point functions lie within an O(1) factor of the values realized in supersymmetric QCD in the conformal window.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Poland, David0000-0003-3854-2430
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2012 SISSA, Trieste, Italy. Received: April 9, 2012. Accepted: May 1, 2012. Published: May 23, 2012. We thank Nima Arkani-Hamed, Diego Hofman, Ken Intriligator, Juan Maldacena, Riccardo Rattazzi, Slava Rychkov, and Matt Strassler for helpful comments and conversations. The computations in this paper were run on the Odyssey cluster supported by the FAS Science Division Research Computing Group at Harvard University. We would like to thank John Brunelle in particular for technical support. This work is supported in part by the Harvard Center for the Fundamental Laws of Nature, NSF grant PHY-0556111, the Swiss National Science Foundation under contract No. 200021-125237, and by the Director, Office of Science, Office of High Energy and Nuclear Physics, of the US Department of Energy under Contract DE-AC02-05CH11231.
Funding AgencyGrant Number
Harvard Center for the Fundamental Laws of NatureUNSPECIFIED
Swiss National Science Foundation (SNSF)200021-125237
Department of Energy (DOE)DE-AC02-05CH11231
Subject Keywords:Conformal and W Symmetry, Supersymmetric gauge theory, Global Symmetries
Issue or Number:5
Record Number:CaltechAUTHORS:20170816-080350610
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Official Citation:Poland, D., Simmons-Duffin, D. & Vichi, A. J. High Energ. Phys. (2012) 2012: 110.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80462
Deposited By: Ruth Sustaita
Deposited On:16 Aug 2017 22:53
Last Modified:15 Nov 2021 19:36

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