Ward Identity implied recursion relations in Yang-Mills theory

TL;DR

This paper derives recursion relations for Yang-Mills amplitudes using Ward identities, enabling efficient calculations even with boundary contributions, and connects these to BCFW recursion at finite poles.

Contribution

It introduces a new recursion relation based on Ward identities that simplifies amplitude calculations in Yang-Mills theory, including cases with boundary terms.

Findings

Recursion relations match BCFW at finite poles.

Boundary terms can be transformed into simple forms.

Effective for amplitudes with off-shell lines.

Abstract

The Ward identity in gauge theory constrains the behavior of the amplitudes. We discuss the Ward identity for amplitudes with a pair of shifted lines with complex momenta. This will induce a recursion relation identical to BCFW recursion relations at the finite poles of the complexified amplitudes. Furthermore, according to the Ward identity, it is also possible to transform the boundary term into a simple form, which can be obtained by a new recursion relation. For the amplitude with one off-shell line in pure Yang-Mills theory, we find this technique is effective for obtaining the amplitude even when there are boundary contributions.