Repairing Broken Algebras

TL;DR

This paper develops a formalism to analyze theories with Ward operators that do not form a closed algebra, deriving conditions for acceptable algebra breaking and applying it to the N=4 supersymmetric nonlinear sigma model.

Contribution

It introduces a method to handle non-closed Ward operator algebras and derives the classical action form under the Slavnov--Taylor identity.

Findings

Derived the form of the classical action with algebra breaking

Expressed the 1PI functional in terms of known quantities

Applied formalism to N=4 supersymmetric nonlinear sigma model

Abstract

We consider theories characterized by a set of Ward operators which do not form a closed algebra. We impose the Slavnov--Taylor identity built out of the Ward operators and we derive the acceptable breaking of the algebra and the general form of the classical action. The 1PI generating functional is expressed in terms of the known quantities characterizing the theory and of a nontrivial integrability condition. As a nontrivial application of our formalism, we discuss the N=4 supersymmetric nonlinear sigma model.