The coupling flow of mathcal{N} = 4 super Yang-Mills theory

Abstract

We offer a novel perspective on mathcal{N} = 4 supersymmetric Yang-Mills (SYM) theory through the framework of the Nicolai map, a transformation of the bosonic fields that allows one to compute quantum correlators in terms of a free, purely bosonic functional measure. Generally, any Nicolai map is obtained through a path-ordered exponential of the so-called coupling flow operator. The latter can be canonically constructed in any gauge using an mathcal{N} = 1 off-shell superfield formulation of mathcal{N} = 4 SYM, or alternatively through dimensional reduction of the result from mathcal{N} = 1 D = 10 SYM, in which case we need to restrict to the Landau gauge. We propose a general theory of the mathcal{N} = 4 coupling flow operator, arguing that it exhibits an ambiguity in form of an R-symmetry freedom given by the Lie algebra mathfrak{su} (4). This theory incorporates our two construction approaches as special points in mathfrak{su} (4) and defines a broad class of Nicolai maps for mathcal{N} = 4 SYM.