On the Vacuum Energy Density and Non-Perturbative Effects in Sigma Models

TL;DR

This paper calculates the vacuum energy density in the $O(N)$ nonlinear sigma model, revealing that non-perturbative effects are linked to the square of the symmetry current, applicable to constrained sigma fields.

Contribution

It demonstrates a connection between non-perturbative contributions and the symmetry current in the $O(N)$ sigma model, providing new insights into vacuum energy calculations.

Findings

Non-perturbative effects relate to the square of the $O(N)$ symmetry current.

Vacuum energy density is explicitly computed for the sigma model.

The results apply to sigma fields with constraints.

Abstract

The vacuum energy density is obtained for the $O(N)$ nonlinear sigma model. It is shown that non-perturbative contributions are connected with the square of the symmetry current of the group $O(N)$. This result is valid for $\sigma$- fields which are subject to the constraint.