Perturbative linearization of super-Yang-Mills theories in general gauges

TL;DR

This paper extends the perturbative construction of the Nicolai map in supersymmetric Yang-Mills theories to a broad class of gauges, providing explicit results beyond the previously known Landau gauge.

Contribution

It generalizes the Nicolai map construction to various gauges and establishes conditions for its validity off the gauge hypersurface, with explicit second and fourth order results.

Findings

Extended Nicolai map to non-Landau gauges

Explicit second-order results in axial gauge

Explicit fourth-order results in Landau gauge

Abstract

Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.