000628934 001__ 628934 000628934 005__ 20250708212234.0 000628934 0247_ $$2INSPIRETeX$$aBarrat:2025nvu 000628934 0247_ $$2inspire$$ainspire:2932014 000628934 0247_ $$2arXiv$$aarXiv:2506.06422 000628934 0247_ $$2datacite_doi$$a10.3204/PUBDB-2025-01738 000628934 037__ $$aPUBDB-2025-01738 000628934 041__ $$aEnglish 000628934 088__ $$2DESY$$aDESY-25-078 000628934 088__ $$2arXiv$$aarXiv:2506.06422 000628934 1001_ $$0P:(DE-H253)PIP1098469$$aBarrat, Julien$$b0$$eCorresponding author 000628934 245__ $$aThe analytic bootstrap at finite temperature 000628934 260__ $$c2025 000628934 3367_ $$0PUB:(DE-HGF)25$$2PUB:(DE-HGF)$$aPreprint$$bpreprint$$mpreprint$$s1751973109_2380178 000628934 3367_ $$2ORCID$$aWORKING_PAPER 000628934 3367_ $$028$$2EndNote$$aElectronic Article 000628934 3367_ $$2DRIVER$$apreprint 000628934 3367_ $$2BibTeX$$aARTICLE 000628934 3367_ $$2DataCite$$aOutput Types/Working Paper 000628934 500__ $$a61 pages 000628934 520__ $$aWe propose new formulae for thermal two-point functions of scalar operators, based ontheir analytic structure at both zero and non-zero spatial separation. At zero spatialseparation, we derive a dispersion relation in the complexified time plane, which fixesthe correlator up to an additive constant and theory-dependent dynamical information.At non-zero spatial separation, we explore the interplay between dispersion relations, theOPE, and the KMS condition. In particular, we introduce a formula for the thermal two-point function obtained by summing over images of the dispersion relation result. Thisconstruction satisfies all thermal bootstrap conditions, with the exception of clustering atinfinite distance, which must be verified on a case-by-case basis. We test our results both inweakly and strongly coupled theories. In particular, we show that the Tauberian behaviorof [1] and its correction can be explicitly derived from dispersion relation. We combineanalytical and numerical results in a “hybrid” bootstrap fashion, and we compute thethermal two-point function of the energy operator in the 3d Ising model and find excellentagreement with Monte Carlo simulations. 000628934 536__ $$0G:(DE-HGF)POF4-611$$a611 - Fundamental Particles and Forces (POF4-611)$$cPOF4-611$$fPOF IV$$x0 000628934 536__ $$0G:(EU-Grant)101044226$$aBrokenSymmetries - Exact Results from Broken Symmetries (101044226)$$c101044226$$fERC-2021-COG$$x1 000628934 536__ $$0G:(GEPRIS)506632645$$aDFG project G:(GEPRIS)506632645 - SFB 1624: Höhere Strukturen, Modulräume und Integrabilität (506632645)$$c506632645$$x2 000628934 536__ $$0G:(GEPRIS)390833306$$aDFG project G:(GEPRIS)390833306 - EXC 2121: Quantum Universe (390833306)$$c390833306$$x3 000628934 588__ $$aDataset connected to INSPIRE 000628934 693__ $$0EXP:(DE-MLZ)NOSPEC-20140101$$5EXP:(DE-MLZ)NOSPEC-20140101$$eNo specific instrument$$x0 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 000628934 8564_ $$uhttps://bib-pubdb1.desy.de/record/628934/files/HTML-Approval_of_scientific_publication.html 000628934 8564_ $$uhttps://bib-pubdb1.desy.de/record/628934/files/PDF-Approval_of_scientific_publication.pdf 000628934 8564_ $$uhttps://bib-pubdb1.desy.de/record/628934/files/2506.06422v1.pdf$$yOpenAccess 000628934 8564_ $$uhttps://bib-pubdb1.desy.de/record/628934/files/2506.06422v1.pdf?subformat=pdfa$$xpdfa$$yOpenAccess 000628934 909CO $$ooai:bib-pubdb1.desy.de:628934$$popenaire$$popen_access$$pdriver$$pVDB$$pec_fundedresources$$pdnbdelivery 000628934 9101_ $$0I:(DE-588b)2008985-5$$6P:(DE-H253)PIP1098469$$aDeutsches Elektronen-Synchrotron$$b0$$kDESY 000628934 9101_ $$0I:(DE-HGF)0$$6P:(DE-H253)PIP1089622$$aExternal Institute$$b1$$kExtern 000628934 9101_ $$0I:(DE-588b)2008985-5$$6P:(DE-H253)PIP1092973$$aDeutsches Elektronen-Synchrotron$$b2$$kDESY 000628934 9101_ $$0I:(DE-588b)2008985-5$$6P:(DE-H253)PIP1103460$$aDeutsches Elektronen-Synchrotron$$b3$$kDESY 000628934 9101_ $$0I:(DE-588b)2008985-5$$6P:(DE-H253)PIP1018308$$aDeutsches Elektronen-Synchrotron$$b4$$kDESY 000628934 9131_ $$0G:(DE-HGF)POF4-611$$1G:(DE-HGF)POF4-610$$2G:(DE-HGF)POF4-600$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$aDE-HGF$$bForschungsbereich Materie$$lMatter and the Universe$$vFundamental Particles and Forces$$x0 000628934 9141_ $$y2025 000628934 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 000628934 9201_ $$0I:(DE-H253)T-20120731$$kT$$lTheorie-Gruppe$$x0 000628934 980__ $$apreprint 000628934 980__ $$aVDB 000628934 980__ $$aUNRESTRICTED 000628934 980__ $$aI:(DE-H253)T-20120731 000628934 9801_ $$aFullTexts