Abstract
Recently, Bjerrum-Bohr, Damgaard, Feng, and Sondergaard derived a set of new interesting quadratic identities of the Yang-Mills (YM) tree scattering amplitudes, besides Bern-Carrasco-Johansson (BCJ) identities. Here we comment that these quadratic identities of YM amplitudes actually follow directly from the KLT (Kawai-Lewellen-Tye) relation for graviton-dilaton-axion scattering amplitudes (in four-dimensional spacetime). This clarifies their physical origin and also provides a simpler version of the new identities. We also comment that the recently discovered BCJ identities of YM helicity amplitudes, at least for the maximal helicity-violating case, 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.
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