Construction method for the Nicolai map in supersymmetric Yang-Mills theories

TL;DR

This paper develops a systematic perturbative method to construct the Nicolai map in supersymmetric Yang-Mills theories, extending previous approaches to arbitrary gauges and providing explicit calculations up to second order.

Contribution

It introduces a full perturbative expansion of the coupling flow operator for the Nicolai map in off-shell supersymmetric Yang-Mills theories, applicable to any gauge.

Findings

Explicit second-order Nicolai map in axial gauge

Extension of construction method to arbitrary gauges

Framework for computing the Nicolai map to any order

Abstract

Recently, a universal formula for the Nicolai map in terms of a coupling flow functional differential operator was found. We present the full perturbative expansion of this operator in Yang-Mills theories where supersymmetry is realized off-shell. Given this expansion, we develop a straightforward method to compute the explicit Nicolai map to any order in the gauge coupling. Our work extends the previously known construction method from the Landau gauge to arbitrary gauges and from the gauge hypersurface to the full gauge-field configuration space. As an example, we present the map in the axial gauge to the second order.