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Bootstrapping the 3d Ising model at finite temperature
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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 $\langle \sigma\sigma \rangle$ and $\langle \epsilon\epsilon \rangle$. As a result, we estimate the one-point functions of the lowest-dimension $\mathbb Z_2$-even scalar $\epsilon$ and the stress-energy tensor $T_{\mu \nu}$. Our result for $\langle \sigma\sigma \rangle$ at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.
Forward citations
Cited by 5 Pith papers
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OPE and QNM representations of the mixed retarded correlator overlap in complex time, giving an explicit map, sum rules, and new QNM asymptotics for large-N thermal CFTs.
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KMS-symmetric thermal Polyakov blocks Fourier-transform into asymptotic retarded correlators, yielding inversion formulae that express thermal OPE coefficients in terms of quasinormal-mode frequencies under meromorphicity.
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The authors derive and test systematic large-dimension asymptotics for heavy-heavy-light OPE coefficients in 3D CFTs from thermal one-point functions on S1 x S2.
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Spin-resolved double-trace thermal coefficients in holography
Zero-frequency bulk Heun solutions fix the residual spatial ambiguity left by KMS, yielding spin-resolved holographic double-trace thermal coefficients and canceling complex bulk-cone singularities.
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Thermal $n$-Point Conformal Blocks in Four Dimensions from Oscillator Representations
New analytic formulas for four-dimensional thermal n-point conformal blocks are derived from oscillator representations, with a correct low-temperature limit to vacuum comb-channel blocks.
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