Does confinement imply CP invariance of the strong interactions?

TL;DR

The paper demonstrates that in SU(3) Yang-Mills theory, the infrared fixed point at zero coupling and theta angle leads to confinement and naturally resolves the strong CP problem by driving theta to zero.

Contribution

It shows that the infrared fixed point at zero coupling and theta angle explains confinement and solves the strong CP problem without additional assumptions.

Findings

Infrared fixed point at $1/g^2=0$, $ heta=0$

Confinement arises from the fixed point behavior

Initial non-zero theta values are driven to zero at large distances

Abstract

The strong coupling constant $1/g^2$ and the vacuum angle $\theta$ of the SU(3) Yang-Mills theory are investigated in the infrared limit under the renormalization group flow. It is shown that the theory has an infrared attractive fixed point at $1/g^2 = \theta = \,0$, which leads to linear confinement and naturally solves the strong CP problem. In particular, any initial value of $\theta \neq 0$ is found to be driven to $\theta = 0$ at macroscopic distances, where quarks and gluons freeze into hadrons by the confinement mechanism.