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<p>We propose new universal formulae for thermal two-point functions of scalar operators based on their analytic structure, constructed to manifestly satisfy all the bootstrap conditions. We derive a dispersion relation in the complexified time plane, which fixes the correlator up to an additive constant and theory-dependent dynamical information. At non-zero spatial separation we introduce a formula for the thermal two-point function obtained by summing over images of the dispersion relation result obtained in the OPE regime. This construction satisfies all thermal bootstrap conditions, with the exception of clustering at infinite distance, which must be verified on a case-by-case basis. We test our results both in weakly and strongly-coupled theories. In particular, we show that the asymptotic behavior for the heavy sector proposed in [<CitationRef CitationID="CR1">1</CitationRef>] and its correction can be explicitly derived from the dispersion relation. We combine analytical and numerical results to compute the thermal two-point function of the energy operator in the 3d Ising model and find agreement with Monte Carlo simulations.</p>

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The analytic bootstrap at finite temperature

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月11日

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  • Julien Barrat,
  • Deniz N. Bozkurt,
  • Enrico Marchetto,
  • Alessio Miscioscia,
  • Elli Pomoni

摘要

We propose new universal formulae for thermal two-point functions of scalar operators based on their analytic structure, constructed to manifestly satisfy all the bootstrap conditions. We derive a dispersion relation in the complexified time plane, which fixes the correlator up to an additive constant and theory-dependent dynamical information. At non-zero spatial separation we introduce a formula for the thermal two-point function obtained by summing over images of the dispersion relation result obtained in the OPE regime. This construction satisfies all thermal bootstrap conditions, with the exception of clustering at infinite distance, which must be verified on a case-by-case basis. We test our results both in weakly and strongly-coupled theories. In particular, we show that the asymptotic behavior for the heavy sector proposed in [1] and its correction can be explicitly derived from the dispersion relation. We combine analytical and numerical results to compute the thermal two-point function of the energy operator in the 3d Ising model and find agreement with Monte Carlo simulations.