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Conformal Field Theories in Fractional Dimensions

El-Showk, Sheer and Paulos, Miguel and Poland, David and Rychkov, Slava and Simmons-Duffin, David and Vichi, Alessandro (2014) Conformal Field Theories in Fractional Dimensions. Physical Review Letters, 112 (14). Art. No. 141601. ISSN 0031-9007. doi:10.1103/PhysRevLett.112.141601.

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We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary conformal field theories connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of ϕ^4 theory in the ϵ expansion.

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:© 2014 American Physical Society. Received 16 December 2013; published 7 April 2014. S. R. is grateful to J. Cardy for useful discussions and to H. W. Diehl for informing him about Refs. [42–44]. We thank the organizers and participants for the stimulating environment at the “Back to the Bootstrap 3” conference at CERN. The work of S. E. was supported by the French ANR Contract No. 05-BLAN-NT09-573739, the ERC Advanced Grant No. 226371, and the ITN program PITN-GA-2009-237920. M. P. is supported by DOE Grant No. DE-SC0010010-Task A. D. P. thanks the Galileo Galilei Institute for Theoretical Physics and the INFN for hospitality and partial support during the completion of this work. 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). The work of D. S. D. is supported by DOE Grant No. DE-SC0009988. D. S.-D. thanks SLAC for hospitality while this work was being completed. This research used resources of the National Energy Research Scientific Computing Center, which is supported, as the work of A. V., by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH1123.
Funding AgencyGrant Number
Agence Nationale pour la Recherche (ANR)05-BLAN-NT09-573739
European Research Council (ERC)226371
Department of Energy (DOE)DE-SC0010010
Department of Energy (DOE)DE-SC0009988
Department of Energy (DOE)DE-AC02-05CH1123
Issue or Number:14
Classification Code:PACS numbers: 11.25.Hf
Record Number:CaltechAUTHORS:20170817-113742628
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Official Citation:Conformal Field Theories in Fractional Dimensions El-Showk, Sheer and Paulos, Miguel and Poland, David and Rychkov, Slava and Simmons-Duffin, David and Vichi, Alessandro}, Phys. Rev. Lett., volume 112, no 14, pages 141601 2014. doi 10.1103/PhysRevLett.112.141601
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80563
Deposited By: Ruth Sustaita
Deposited On:18 Aug 2017 21:34
Last Modified:15 Nov 2021 19:37

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