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The Conformal Bootstrap at Finite Temperature

Iliesiu, Luca and Koloğlu, Murat and Mahajan, Raghu and Perlmutter, Eric and Simmons-Duffin, David (2018) The Conformal Bootstrap at Finite Temperature. Journal of High Energy Physics, 2018 (10). Art. No. 070. ISSN 1126-6708. doi:10.1007/JHEP10(2018)070.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Iliesiu, Luca0000-0001-7567-7516
Koloğlu, Murat0000-0002-5082-8434
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2018 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: August 23, 2018; Accepted: October 5, 2018; Published: October 9, 2018. We thank Chris Beem, Simon Caron-Huot, Sergei Gukov, Martin Hasenbusch, Jared Kaplan, Zohar Komargodski, Petr Kravchuk, Juan Maldacena, Alex Maloney, Shiraz Minwalla, Silviu Pufu, Slava Rychkov, Subir Sachdev, Nati Seiberg, Douglas Stanford, and Sasha Zhiboedov for discussions. We especially thank Martin Hasenbusch for sharing unpublished results, and for valuable discussions. DSD, EP, and MK are supported by Simons Foundation grant 488657, and by the Walter Burke Institute for Theoretical Physics. RM is supported by US Department of Energy grant No. DE-SC0016244. LVI is supported by Simons Foundation grant 488653.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation488657
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Department of Energy (DOE)DE-SC0016244
Simons Foundation488653
Subject Keywords:Conformal Field Theory, Field Theories in Higher Dimensions
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Issue or Number:10
Record Number:CaltechAUTHORS:20180305-134232971
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Official Citation:Iliesiu, L., Koloğlu, M., Mahajan, R. et al. J. High Energ. Phys. (2018) 2018: 70.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85101
Deposited By: Joy Painter
Deposited On:05 Mar 2018 21:54
Last Modified:15 Nov 2021 20:25

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