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Peer-reviewedCC BYJournal of High Energy Physics

The analytic bootstrap at finite temperature

  • Julien Barrat1
  • Deniz N. Bozkurt2
  • Enrico Marchetto1
  • Alessio Miscioscia1
  • Elli Pomoni1
  1. 1Deutsches Elektronen-Synchrotron DESY
  2. 2Universität Hamburg
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Abstract

A bstract 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.

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Cite

BibTeXRIS
BibTeX
@article{barrat2026analytic,
  title = {{The analytic bootstrap at finite temperature}},
  author = {Julien Barrat and Deniz N. Bozkurt and Enrico Marchetto and Alessio Miscioscia and Elli Pomoni},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = may,
  doi = {10.1007/jhep05(2026)104},
  url = {https://doi.org/10.1007/jhep05(2026)104},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - The analytic bootstrap at finite temperature
AU  - Julien Barrat
AU  - Deniz N. Bozkurt
AU  - Enrico Marchetto
AU  - Alessio Miscioscia
AU  - Elli Pomoni
PY  - 2026
DA  - 2026/05/11
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep05(2026)104
UR  - https://doi.org/10.1007/jhep05(2026)104
AB  - A bstract 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.
SN  - 1029-8479
SN  - 1126-6708
SN  - 1127-2236
ER  -