Gravitationally dressed Parke-Taylor

A generating function for the Parke-Taylor amplitudes with any number of positive helicity gravitons in addition to the positive helicity gluons is obtained using the recently constructed self-dual classical solution of the type of perturbiner in Yang-Mills theory interacting with gravity. Computation of multi-particle amplitudes in gauge theories in the leading and next-to-leading orders has turned into the whole industry. There is permanent technological progress in the canonical Feynman perturbation theory direction (see, e.g., the reviews [1], [2]) and there are also alternative directions like the string inspired technique (see, e.g. the review [3]) and the world-line technique ([4]). Our favorite approach is based on the so-called perturbiners (ptb). Ptbs are solutions of field equations which are generating functions for tree form-factors in the theory. The ptb solution can be given an intrinsic definition [5] which is formally independent of the Feynman diagrams. In words it sounds as follows. Take a solution of the free (linear) field equation in the theory under consideration in the form of superposition of a set of plane waves. Regard every plane wave as nilpotent. The corresponding ptb is a solution of the full (nonlinear) field equation which is polynomial in the plane waves, first order term of the polynomial being just the solution of the free field equation. The plane waves are nothing but the asymptotic wave functions of the one-particle states included in the form-factors which the ptb is the generating function for. The nilpotency assumes that the ptb is