Further Comments on the Symmetric Subtraction of the Nonlinear Sigma Model

TL;DR

This paper proves that a symmetric subtraction method for divergences in the nonlinear sigma model is valid to all orders and discusses the limitation of using only two physical parameters within this framework.

Contribution

It provides a formal proof of the all-order symmetry of the divergence subtraction procedure in the nonlinear sigma model.

Findings

The subtraction method is symmetric at all loop orders.

Only two parameters can be consistently used as physical constants.

The approach overcomes non chiral symmetric divergences at one loop and beyond.

Abstract

Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled to the nonlinear sigma model constraint (flat connection formalism). The construction is based on a local functional equation, which overcomes the problems due to the presence (already at one loop) of non chiral symmetric divergences. The subtraction procedure of the divergences in the loop expansion is performed by means of minimal subtraction of properly normalized amplitudes in dimensional regularization. In this paper we complete the study of this subtraction procedure by giving the formal proof that it is symmetric to all orders in the loopwise expansion. We provide further arguments on the issue that, within our subtraction strategy, only two parameters can be consistently used as physical constants.