Comment on the Identities of the Gluon Tree Amplitudes

TL;DR

This paper explains the origin of recent quadratic identities in Yang-Mills amplitudes through KLT relations, clarifies their physical basis, and discusses related identities and verification methods.

Contribution

It reveals that quadratic identities of YM amplitudes derive from KLT relations and offers a simpler understanding, also commenting on B-C-J identities and additional identities.

Findings

Quadratic identities follow from KLT relations.

B-C-J identities verified via Schouten identity.

Additional identities can be derived from KLT relations.

Abstract

Recently, Bjerrum-Bohr, Damgaard, Feng and Sondergaard derived a set of new interesting quadratic identities of the Yang-Mills tree scattering amplitudes. Here we comment that these quadratic identities of YM amplitudes actually follow directly from the KLT relation for graviton-dilaton-axion scattering amplitudes (in 4 dimensional spacetime). This clarifies their physical origin and also provides a simpler version of the new identities. We also comment that the recently discovered Bern-Carrasco-Johansson identities of YM helicity amplitudes can be verified by using (repeatedly) the Schouten identity. We also point out additional quadratic identities that can be written down from the KLT relations.