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Elliptical Wilson loops in N=4 Super Yang-Mills theory

Thales Azevedo1,2,*, Alfonso Ballon-Bayona1,†, and Leonardo Pazito1,‡

  • *Contact author: thales@if.ufrj.br
  • †Contact author: aballonb@if.ufrj.br
  • ‡Contact author: lmpazito@pos.if.ufrj.br
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Phys. Rev. D 112, 126018 – Published 19 December, 2025

DOI: https://doi.org/10.1103/53y8-72hr

Abstract

We investigate elliptical Wilson loops in N=4 Super Yang–Mills theory at weak and strong coupling for small values of the eccentricity. We obtain analytical results for the vacuum expectation value of the Wilson loop in the form of a series in the eccentricity parameter. At weak coupling, we use perturbation theory in N=4 Super Yang–Mills. At strong coupling, we use the AdS/CFT correspondence, which maps the Wilson loop to the minimal-area world sheet of an open string in anti–de Sitter (AdS) space. We present a novel perturbative method to solve the Nambu–Goto equations allowing us to describe the minimal surface in terms of a coordinate parametrization in Euclidean AdS3. Our results for the regularized area agree with those obtained by Dekel [J. High Energy Phys. 03 (2015) 085.] based on the Polyakov action.

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Phys. Rev. D 112, 126018– Published 19 December, 2025
  • Received 16 October 2025
  • Accepted 24 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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