Dynamics of Finite-Temperature CFTs from OPE Inversion Formulas

Abstract

We apply the OPE inversion formula to thermal two-point functions of bosonic and fermionic CFTs in general odd dimensions. This allows us to analyze in detail the operator spectrum of these theories. We find that nontrivial thermal CFTs arise when the thermal mass satisfies an algebraic transcendental equation that ensures the absence of an infinite set of operators from the spectrum. The solutions of these gap equations for general odd dimensions are in general complex numbers and follow a particular pattern. We argue that this pattern unveils the large-$N$ vacuum structure of the corresponding theories at zero temperature.

arXiv comment5 pages. v2: Typos fixed

References in corpus (6)

• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model
• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• C_{T} and C_{J} up to next-to-leading order in 1/N in the Conformally Invariant O(N) Vector Model for 2<d<4
• Six dimensional QCD at two loops
• Finite-Size Effects and Operator Product Expansions in a CFT for d>2

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