Universal aspects of perturbative gauge theory - Frost, H (2020)
Gravity amplitudes, at tree level, can be computed from gauge theory amplitudes using the (field theory) KLT relation. Underlying the KLT relation are the `Kleiss-Kuijf' and 'fundamental BCJ' identities satisfied by gauge theory partial amplitudes. These identities, and the KLT relation, are proved in an elementary way using properties of Lie polynomials, and the properties of a Lie bracket we call the 'S bracket', which has appeared in examples in superstring calculations. The S bracket is also closely related to string-like formulas which express partial amplitudes as sums of residues of rational functions on M0,n. In this context, identities amoung rational functions on M0,n allow us to prove a formula for non-linear sigma model partial amplitudes.