Note on the Off-Shell Equivalence between the Linear and Non-Linear Sigma Models

TL;DR

This paper discusses the detailed conditions under which the linear and non-linear O(N) sigma models are equivalent off-shell, extending the known on-shell correspondence to a more general setting.

Contribution

It provides detailed analysis and conditions necessary for establishing off-shell equivalence between linear and non-linear sigma models.

Findings

Off-shell equivalence conditions derived for the models.

Clarification of parameter arrangements for equivalence.

Extension of known on-shell results to off-shell case.

Abstract

As is well known, one can arrange the parameters of the O(N) non-linear sigma model to reproduce the low energy S-matrix elements of the renormalizable O(N) linear sigma model. In this note we provide details which are necessary in order to obtain the off-shell equivalence between the two theories.