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The conformal bootstrap at finite temperature

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 09 October 2018
  • Volume 2018, article number 70, (2018)
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Journal of High Energy Physics Aims and scope Submit manuscript
The conformal bootstrap at finite temperature
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  • Luca Iliesiu1,
  • Murat Koloğlu2,
  • Raghu Mahajan1,3,
  • Eric Perlmutter2 &
  • …
  • David Simmons-Duffin2 

  • 1051 Accesses

  • 101 Citations

  • 12 Altmetric

  • 1 Mention

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A preprint version of the article is available at arXiv.

Abstract

We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a “thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O(N) model at leading order in 1/N. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.

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Authors and Affiliations

  1. Department of Physics, Princeton University, Jadwin Hall, Princeton, NJ, 08540, U.S.A.

    Luca Iliesiu & Raghu Mahajan

  2. Walter Burke Institute for Theoretical Physics, Caltech, 1200 E. California Blvd., Pasadena, CA, 91125, U.S.A.

    Murat Koloğlu, Eric Perlmutter & David Simmons-Duffin

  3. School of Natural Sciences, Institute for Advanced Study, 1 Einstein Dr., Princeton, NJ, 08540, U.S.A.

    Raghu Mahajan

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  1. Luca Iliesiu
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  2. Murat Koloğlu
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  3. Raghu Mahajan
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  5. David Simmons-Duffin
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Correspondence to Eric Perlmutter.

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ArXiv ePrint: 1802.10266

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Iliesiu, L., Koloğlu, M., Mahajan, R. et al. The conformal bootstrap at finite temperature. J. High Energ. Phys. 2018, 70 (2018). https://doi.org/10.1007/JHEP10(2018)070

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  • Received: 23 August 2018

  • Accepted: 05 October 2018

  • Published: 09 October 2018

  • DOI: https://doi.org/10.1007/JHEP10(2018)070

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Keywords

  • Conformal Field Theory
  • Field Theories in Higher Dimensions
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