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

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.

arXiv comment11 pages; v2: two paragraphs added in the introduction, 2 references added, matches published version

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Cited by in corpus (4)

• An improved Nicolai map for super Yang-Mills theory
• Is the Nicolai map unique?
• Nicolai maps for super Yang-Mills on the light cone
• Supersymmetric large-order perturbation with the Nicolai map