Deformations of the circular Wilson loop and spectral (in)dependence

Abstract

In this paper we study the expectation value of deformations of the circular Wilson loop in $\mathcal{N}=4$ super Yang-Mills theory. The leading order deformation, known as the Bremsstrahlung function, can be obtained exactly from supersymmetric localization, so our focus is on deformations at higher orders. We find simple expressions for the expectation values for generic deformations at the quartic order at one-loop at weak coupling and at leading order at strong coupling. We also present a very simple algorithm (not requiring integration) to evaluate the two-loop result. We find that an exact symmetry of the strong coupling sigma-model, known as the spectral-parameter independence, is an approximate symmetry at weak coupling, modifying the expectation value starting only at the sextic order in the deformation. Furthermore, we find very simple patterns for how the spectral parameter can appear in the weak coupling calculation, suggesting all-order structures.

arXiv comment25 pages. v2: minor correction and added (with sincere appologies) missing acknowlegments

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• Semiclassical $p$-branes in hyperbolic space
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories