Perturbative linearization of supersymmetric Yang-Mills theory

TL;DR

This paper extends the perturbative Nicolai map in supersymmetric Yang-Mills theory to third order, providing a diagrammatic approach that simplifies calculations and offers new insights into supersymmetric gauge theories.

Contribution

It introduces a third-order extension of the Nicolai map and a diagrammatic formalism that avoids anti-commuting variables, enhancing understanding of supersymmetric gauge theories.

Findings

Extended Nicolai map to third order in coupling constant

Developed a diagrammatic approach using tree diagrams

Provided a new perspective on supersymmetric gauge theories

Abstract

Supersymmetric gauge theories are characterized by the existence of a transformation of the bosonic fields (Nicolai map) such that the Jacobi determinant of the transformation equals the product of the Matthews-Salam-Seiler and Faddeev-Popov determinants. This transformation had been worked out to second order in the coupling constant. In this paper, we extend this result (and the framework itself) to third order in the coupling constant. A diagrammatic approach in terms of tree diagrams, aiming to extend this map to arbitrary orders, is outlined. This formalism bypasses entirely the use of anti-commuting variables, as well as issues concerning the (non-)existence of off-shell formulations for these theories. It thus offers a fresh perspective on supersymmetric gauge theories and, in particular, the ubiquitous $\mathcal N{=}\,4$ theory.