Dynamics of Finite-Temperature CFTs from OPE Inversion Formulas

TL;DR

This paper uses OPE inversion formulas to analyze the operator spectrum of finite-temperature conformal field theories in odd dimensions, revealing conditions for nontrivial thermal phases and insights into their vacuum structure.

Contribution

It introduces a method to determine the operator spectrum of thermal CFTs using OPE inversion formulas and uncovers the pattern of solutions to the gap equations across odd dimensions.

Findings

Nontrivial thermal CFTs occur when thermal mass satisfies a specific algebraic equation.

Solutions to the gap equations are generally complex and follow a particular pattern.

The pattern of solutions provides insights into the large-N vacuum structure at zero temperature.

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.