Nicolai maps and uniqueness in the light-cone gauge

We compute the Nicolai map for the supersymmetric Yang-Mills theory, in the light-cone gauge, to the second order in the coupling constant for all critical dimensions (d = 3, 4, 6, 10). The process of integrating out unphysical degrees of freedom in this gauge, produces a four fermion interaction term. We show that, to the order investigated here, this term is harmless. We demonstrate the existence of a particularly ‘simple’ map in d = 4 in the light-cone gauge and address the issue of uniqueness in the context of the map. We also investigate the map in the light-cone superspace in d = 4.