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Title: Bootstrapping the 3d Ising model at finite temperature

Abstract

We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions (σσ) and (ϵϵ). As a result, we estimate the one-point functions of the lowest-dimension $$\mathbb{Z}_2$$-even scalar ϵ and the stress energy tensor T μν. Our result for (σσ) at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.

Authors:
 [1];  [2];  [2]
  1. Princeton Univ., NJ (United States)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Research Org.:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1594255
Grant/Contract Number:  
SC0019085
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 12; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Field Theories in Lower Dimensions

Citation Formats

Iliesiu, Luca, Koloğlu, Murat, and Simmons-Duffin, David. Bootstrapping the 3d Ising model at finite temperature. United States: N. p., 2019. Web. doi:10.1007/JHEP12(2019)072.
Iliesiu, Luca, Koloğlu, Murat, & Simmons-Duffin, David. Bootstrapping the 3d Ising model at finite temperature. United States. doi:10.1007/JHEP12(2019)072.
Iliesiu, Luca, Koloğlu, Murat, and Simmons-Duffin, David. Mon . "Bootstrapping the 3d Ising model at finite temperature". United States. doi:10.1007/JHEP12(2019)072. https://www.osti.gov/servlets/purl/1594255.
@article{osti_1594255,
title = {Bootstrapping the 3d Ising model at finite temperature},
author = {Iliesiu, Luca and Koloğlu, Murat and Simmons-Duffin, David},
abstractNote = {We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions (σσ) and (ϵϵ). As a result, we estimate the one-point functions of the lowest-dimension $\mathbb{Z}_2$-even scalar ϵ and the stress energy tensor Tμν. Our result for (σσ) at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.},
doi = {10.1007/JHEP12(2019)072},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2019,
place = {United States},
year = {2019},
month = {12}
}

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