On Tree Form-Factors¶in (Supersymmetric) Yang–Mills Theory

Abstract:

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 works by E. Witten [1] and by J. Isenberg, P. B. Yasskin and P. S. Green [2].