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arXiv · 2206.02919

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

Hannes Malcha
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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.

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Hannes Malcha. 2022-08-22. Two Loop Ghost free Quantisation of Wilson Loops in $\mathcal{N}=4$ supersymmetric Yang-Mills. https://doi.org/10.1016/j.physletb.2022.137377

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