ar X iv : h ep - t h / 98 09 04 6 v 2 2 1 M ay 1 99 9 On tree form - factors in ( supersymmetric ) Yang - Mills theory

Perturbiner, that is, the solution of field equations which is a generating function for tree form-factors in N = 3 (N = 4) supersymmetric Yang-Mills theory, is studied in the framework of twistor formulation of the N = 3 superfield equations. In the case, when all one-particle asymptotic states belong to the same type of N = 3 supermultiplets (without any restriction on kinematics), the solution is described very explicitly. It happens to be a natural supersymmetrization of the self-dual perturbiner in non-supersymmetric Yang-Mills theory, designed to describe the Parke-Taylor amplitudes. In the general case, we reduce the problem to a neatly formulated algebraic geometry problem (see Eqs(70),(71),(72)) and propose an iterative algorithm for solving it, however we have not been able to find a closed-form solution. Solution of this problem would, of course, produce a description of all tree form-factors in non-supersymmetric Yang-Mills theory as well. In this context, the N = 3 superfield formalism may be considered as a convenient way to describe a solution of the non-supersymmetric Yang-Mills theory, very much in the spirit of [1], [2].