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 twister formulation of the N = 3 sup erfield equations. In the case when all one-particle asymptotic states belo ng to the same type of N = 3 supermultiplets (without any restriction on ki nematics), the solution is described very explicitly. It happens to be a na tural supersymmetrization of the self-dual perturbiner in non-supersymmetri c Yang-Mills theory, designed to describe the Parke-Taylor amplitudes. In t he general case, we reduce the problem to a neatly formulated algebraic geo metry problem (see Eqs. (70), (71), (72)) and propose an iterative algorith m for solving it, however we have not been able to find a closed-form solut ion. Solution of this problem would, of course, produce a description of al l tree form-factors in non-supersymmetric Yang-Mills theory as well. In thi s context, the N = 3 superfield formalism may be considered as a convenient way to describe a solution of the non-supersymmetric Yang-Mills theory, ve ry much in the spirit of works by E. Witten [1] and by J. Isenberg, P. B. Y asskin and P. S. Green [2].