Nicolai maps and uniqueness in the light-cone gauge

TL;DR

This paper computes the Nicolai map for supersymmetric Yang-Mills theory in the light-cone gauge across multiple dimensions, demonstrating its existence, simplicity in four dimensions, and addressing the issue of uniqueness.

Contribution

It provides the explicit second-order Nicolai map in light-cone gauge for all critical dimensions and discusses its uniqueness and simplicity in four dimensions.

Findings

The Nicolai map exists to second order in all critical dimensions.

The four-fermion interaction term is harmless at this order.

A particularly simple map is demonstrated in four dimensions.

Abstract

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.