Renormalization Group Flow and Thermodynamics of Conformal Field Theories

TL;DR

This paper explores the renormalization group flow and thermodynamics of three-dimensional conformal field theories, constructing a trajectory connecting free and interacting theories, and revealing a specific ratio of free-energy densities at a special point.

Contribution

It introduces a method to interpolate between free and strongly coupled conformal theories in D=3, providing insights into their thermodynamic properties and potential applications to other theories.

Findings

Constructed a stationary RG trajectory between free and interacting theories.

Found the free-energy density at a special point is 5/4 times that of the O(N) model.

Method may be applicable to other strongly coupled fixed point theories.

Abstract

We discuss the free-energy density of bosonic and fermionic theories possessing strongly coupled critical points in D=3. We construct a stationary renormalization group trajectory which interpolates between the free massless theory of N scalars and a class of interacting theories including both bosons and fermions. At a special point of this trajectory the free-energy density is 5/4 times the free-energy density of the O(N) vector model at its nontrivial critical point. Our method could in principle be useful in the study of other theories with strongly coupled fixed points, such as {\cal N}=4 SYM in D=4.