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000628934 1001_ $$0P:(DE-H253)PIP1098469$$aBarrat, Julien$$b0$$eCorresponding author
000628934 245__ $$aThe analytic bootstrap at finite temperature
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000628934 520__ $$aWe 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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000628934 7001_ $$0P:(DE-H253)PIP1089622$$aBozkurt, Deniz$$b1
000628934 7001_ $$0P:(DE-H253)PIP1092973$$aMarchetto, Enrico$$b2
000628934 7001_ $$0P:(DE-H253)PIP1103460$$aMiscioscia, Alessio$$b3
000628934 7001_ $$0P:(DE-H253)PIP1018308$$aPomoni, Elli$$b4
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