Two Loop Ghost free Quantisation of Wilson Loops in $\mathcal{N}=4$ supersymmetric Yang-Mills

TL;DR

This paper extends the perturbative calculation of the Maldacena-Wilson loop in N=4 supersymmetric Yang-Mills theory to order g^6, using the Nicolai map to simplify the functional measure, revealing non-trivial cancellations.

Contribution

It introduces a novel approach using the Nicolai map for higher-order perturbative calculations of Wilson loops in N=4 SYM, extending previous results by one order.

Findings

Perturbative cancellations are complex and resemble those at lower order.

The Nicolai map approach is competitive with standard diagrammatic methods.

Extended the order of perturbative calculation to g^6 for the Wilson loop.

Abstract

We report a perturbative calculation of the expectation value of the infinite straight line Maldacena-Wilson loop in $\mathcal{N}=4$ supersymmetric Yang-Mills theory to order $g^6$. Thus, we extend the previous perturbative result by one order. The vacuum expectation value is reformulated in terms of a non-linear and non-local transformation, the Nicolai map, mapping the full functional measure of the interacting theory to that of a free bosonic theory. The results are twofold. The perturbative cancellations of the different contributions to the Maldacena-Wilson loop are by no means trivial and seem to resemble those of the circular Maldacena-Wilson loop at order $g^4$. Furthermore, we argue that our approach to computing quantum correlation functions is competitive with more standard diagrammatic techniques.