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Bootstrapping the 3d Ising model at finite temperature

Iliesiu, Luca·Koloğlu, Murat·Simmons-Duffin, David
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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.

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDSConformal Field TheoryField Theories in Lower Dimensions

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Iliesiu, Luca, Koloğlu, Murat, Simmons-Duffin, David. 2019-12-09. Bootstrapping the 3d Ising model at finite temperature. https://doi.org/10.1007/jhep12(2019)072

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