Non linear $\sigma$ models : renormalisability versus geometry

TL;DR

This paper explores the renormalisability of non-linear sigma models, emphasizing the role of B.R.S. symmetry and the importance of defining theories through physical constraints rather than fixed Lagrangians.

Contribution

It introduces new perspectives on renormalisability in non-linear sigma models by incorporating B.R.S. symmetry and redefining theory formulation via physical constraints.

Findings

B.R.S. symmetry aids in understanding renormalisation

Physical constraints are crucial for defining theories

Proposes ways to extend the concept of renormalisability

Abstract

After some recalls on the standard (non)-linear $\sigma$ model, we discuss the interest of B.R.S. symmetry in non-linear $\sigma$ models renormalisation. We also emphasise the importance of a correct definition of a theory through physical constraints rather than as given by a particular Lagrangian and discuss some ways to enlarge the notion of renormalisability.