Off-shell Ward identities for N-gluon amplitudes

TL;DR

This paper derives the form of off-shell Ward identities for one-loop N-gluon amplitudes in non-abelian gauge theory using the string-inspired formalism, highlighting gauge-fixing dependence and the pinch technique.

Contribution

It provides a new derivation of off-shell Ward identities for N-gluon amplitudes using the string-inspired formalism and background-field method.

Findings

Derived the Ward identity for one-loop N-gluon amplitudes.

Connected the formalism to the pinch technique and background-field method.

Clarified gauge-fixing dependence in off-shell Ward identities.

Abstract

Off-shell Ward identities in non-abelian gauge theory continue to be a subject of active research, since they are, in general, inhomogeneous and their form depends on the chosen gauge-fixing procedure. For the three-gluon and four-gluon vertices, it is known that a relatively simple form of the Ward identity can be achieved using the pinch technique or, equivalently, the background-field method with quantum Feynman gauge. The latter is also the gauge-fixing underlying the string-inspired formalism, and here we use this formalism to derive the corresponding form of the Ward identity for the one-loop N - gluon amplitudes.