Bootstrapping phase transitions in QCD and frustrated spin systems

TL;DR

This paper uses conformal bootstrap methods to provide non-perturbative evidence for the existence of certain fixed points in $O(n)\times O(2)$-symmetric conformal field theories in 3D, relevant for phase transitions in QCD and spin systems.

Contribution

It offers the first non-perturbative evidence for the fixed points in these theories, clarifying the nature of phase transitions in QCD and frustrated spin systems.

Findings

Identifies singular behaviors indicating chiral and collinear fixed points.

Finds no evidence for the anti-chiral fixed point.

Suggests phase transitions are continuous with specific critical exponents.

Abstract

In view of its physical importance in predicting the order of chiral phase transitions in QCD and frustrated spin systems, we perform the conformal bootstrap program of $O(n)\times O(2)$-symmetric conformal field theories in $d=3$ dimensions with a special focus on $n=3$ and $4$. The existence of renormalization group fixed points with these symmetries has been controversial over years, but our conformal bootstrap program provides the non-perturbative evidence. In both $n=3$ and $4$ cases, we find singular behaviors in the bounds of scaling dimensions of operators in two different sectors, which we claim correspond to chiral and collinear fixed points, respectively. In contrast to the cases with larger values of $n$, we find no evidence for the anti-chiral fixed point. Our results indicate the possibility that the chiral phase transitions in QCD and frustrated spin systems are continuous with the critical exponents that we predict from the conformal bootstrap program.