Hot Conformal Gauge Theories

TL;DR

This paper calculates the free energy of conformal SU(N) gauge theories at finite temperature up to high order, revealing a universal critical flavor number signaling potential system instability.

Contribution

It provides a high-order perturbative analysis of the free energy in conformal gauge theories, linking sign changes to the conformal window boundaries.

Findings

The reduced free energy changes sign at specific orders when decreasing flavors.

The critical flavor number matches previous lower boundary predictions at order g^2.

Higher order calculations suggest a larger critical flavor number.

Abstract

We compute the nonzero temperature free energy up to the order g^6 \ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged in such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Due to large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors and matter representation. We show that the reduced free energy changes sign, at the second, fifth and sixth order in the coupling, when decreasing the number of flavors from the upper end of the conformal window. If the change in sign is interpreted as signal of an instability of the system then we infer a critical number of flavors. Surprisingly this number, if computed to the order g^2, agrees with previous predictions for the lower boundary of the conformal window for nonsupersymmetric gauge theories. The higher order results tend to predict a higher number of critical flavors. These are universal properties, i.e. they are independent on the specific matter representation.