Bootstrapping the 3d Ising model at finite temperature

Journal Article · Mon Dec 09 00:00:00 EST 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP12(2019)072· OSTI ID:1594255

Iliesiu, Luca ^[1]; Koloğlu, Murat ^[2]; Simmons-Duffin, David ^[2]

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1. Princeton Univ., NJ (United States)
2. California Inst. of Technology (CalTech), Pasadena, CA (United States)

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.

• Research Organization: California Institute of Technology (CalTech), Pasadena, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0019085
• OSTI ID: 1594255
• Journal Information: Journal of High Energy Physics (Online), Vol. 2019, Issue 12; ISSN 1029-8479
• Publisher: Springer Berlin
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Conformal Field Theory
Field Theories in Lower Dimensions