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2018

Bootstrapping the 3d Ising model at finite temperature

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

Understand

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 $\langle \sigma\sigma \rangle$ and $\langle \epsilon\epsilon \rangle$.