Vacuum structure of CP^N sigma models at theta=pi

TL;DR

This paper demonstrates that parity symmetry remains unbroken in CP^N sigma models at theta equals pi, using a non-perturbative analysis of the vacuum structure and sphaleron effects, constraining the models' critical behavior.

Contribution

It provides a non-perturbative proof that parity is not spontaneously broken at theta=pi in CP^N sigma models, highlighting the role of sphalerons.

Findings

Parity symmetry is not spontaneously broken at theta=pi.

Sphalerons play a crucial role in the vacuum structure.

Constraints on critical behavior at theta=pi.

Abstract

We show that parity symmetry is not spontaneously broken in the CP^N sigma model for any value of N when the coefficient of the $\theta$--term becomes $\theta=\pi$ (mod $2\pi$). The result follows from a non-perturbative analysis of the nodal structure of the vacuum functional $\psi_0(z)$. The dynamical role of sphalerons turns out to be very important for the argument. The result introduces severe constraints on the possible critical behavior of the models at $\theta=\pi$ (mod $2\pi$).