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Sum rules & Tauberian theorems at finite temperature
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We study CFTs at finite temperature and derive explicit sum rules for one-point functions of operators by imposing the KMS condition. In the case of a large gap between light and heavy operators, we explicitly compute one-point functions for light operators. Turning to heavy operators we employ Tauberian theorems and compute the asymptotic OPE density for heavy operators, from which we extract the leading terms of the OPE coefficients associated with heavy operators. Furthermore, we approximate and establish bounds for the two-point functions.
Forward citations
Cited by 8 Pith papers
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OPE = QNM
OPE and QNM representations of the mixed retarded correlator overlap in complex time, giving an explicit map, sum rules, and new QNM asymptotics for large-N thermal CFTs.
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Retarded correlators of displacement operators on line defects in holographic thermal CFTs exhibit bouncing singularities that match between interior-sensitive WKB and boundary-only OPE analyses.
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The analytic bootstrap at finite temperature
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