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

  • Michael Cooke
  • Amit Dekel
  • Nadav DrukkerEmail author
  • Diego Trancanelli
  • Edoardo Vescovi
Open Access
Regular Article - Theoretical Physics


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.


Wilson, ’t Hooft and Polyakov loops AdS-CFT Correspondence Conformal and W Symmetry Integrable Field Theories 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of MathematicsKing’s College LondonLondonUnited Kingdom
  2. 2.Nordita, KTH Royal Institute of Technology and Stockholm UniversityStockholmSweden
  3. 3.Institute of PhysicsUniversity of São PauloSão PauloBrazil
  4. 4.The Blackett LaboratoryImperial CollegeLondonUnited Kingdom

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