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| Preprint | PUBDB-2025-01738 |
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2025
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Please use a persistent id in citations: doi:10.3204/PUBDB-2025-01738
Report No.: DESY-25-078; arXiv:2506.06422
Abstract: We propose new formulae for thermal two-point functions of scalar operators, based ontheir analytic structure at both zero and non-zero spatial separation. At zero spatialseparation, we derive a dispersion relation in the complexified time plane, which fixesthe correlator up to an additive constant and theory-dependent dynamical information.At non-zero spatial separation, we explore the interplay between dispersion relations, theOPE, and the KMS condition. In particular, we introduce a formula for the thermal two-point function obtained by summing over images of the dispersion relation result. Thisconstruction satisfies all thermal bootstrap conditions, with the exception of clustering atinfinite distance, which must be verified on a case-by-case basis. We test our results both inweakly and strongly coupled theories. In particular, we show that the Tauberian behaviorof [1] and its correction can be explicitly derived from dispersion relation. We combineanalytical and numerical results in a “hybrid” bootstrap fashion, and we compute thethermal two-point function of the energy operator in the 3d Ising model and find excellentagreement with Monte Carlo simulations.
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