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Solving the 3D Ising model with the conformal bootstrap

El-Showk, Sheer and Paulos, Miguel F. and Poland, David and Rychkov, Slava and Simmons-Duffin, David and Vichi, Alessandro (2012) Solving the 3D Ising model with the conformal bootstrap. Physical Review D, 86 (2). Art. No. 025022. ISSN 1550-7998.

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We study the constraints of crossing symmetry and unitarity in general 3D conformal field theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for their computation in arbitrary space-time dimension. Comparing the resulting bounds on operator dimensions and product-expansion coefficients in 3D to known results, we find that the 3D Ising model lies at a corner point on the boundary of the allowed parameter space. We also derive general upper bounds on the dimensions of higher spin operators, relevant in the context of theories with weakly broken higher spin symmetries.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Poland, David0000-0003-3854-2430
Rychkov, Slava0000-0002-5847-1011
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2012 American Physical Society. Received 22 May 2012; published 20 July 2012 We are grateful to Juan Maldacena, Hugh Osborn, and Mohammad Rajabpour for useful discussions. The work of S. R. is supported in part by the European Program Unification in the LHC Era, Contract No. PITN-GA-2009-237920 (UNILHC), and by the Émergence-UPMC-2011 research program. The work of D. P. is supported by DOE Grant No. DE-FG02-90ER40542. The work of A. V. is supported by the Office of High Energy Physics of the U.S. Department of Energy under the Contract No. DE-AC02-05CH1123. The work of S. E. is supported primarily by the Netherlands Organization for Scientific Research (NWO) under a Rubicon grant and also partially by the ERC Starting Independent Researcher Grant No. 240210-String-QCD-BH.
Funding AgencyGrant Number
Marie Curie FellowshipPITN-GA-2009-237920
Department of Energy (DOE)DE-FG02-90ER40542
Department of Energy (DOE)DE-AC02-05CH11231
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)UNSPECIFIED
European Research Council (ERC)240210-String-QCD-BH
Issue or Number:2
Classification Code:PACS numbers: 11.25.Hf, 64.60.F
Record Number:CaltechAUTHORS:20170817-113623391
Persistent URL:
Official Citation:Solving the 3D Ising model with the conformal bootstrap Sheer El-Showk, Miguel F. Paulos, David Poland, Slava Rychkov, David Simmons-Duffin, and Alessandro Vichi Phys. Rev. D 86, 025022 (2012) – Published 20 July 2012
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80562
Deposited By: Ruth Sustaita
Deposited On:18 Aug 2017 21:34
Last Modified:20 Nov 2020 20:05

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