Elliptical Wilson loops in \cal N=4 Super Yang-Mills

2025/09/04 by Azevedo, Thales, Ballon-Bayona, Alfonso, Pazito, Leonardo
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2509.04355

Abstract

We investigate elliptical Wilson loops in \cal 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 \cal N=4 Super Yang--Mills. At strong coupling, we use the AdS/CFT correspondence, which maps the Wilson loop to the minimal-area worldsheet of an open string in 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 parameterization in Euclidean AdS₃. Our results for the regularized area agree with those obtained by Dekel in [1] based on the Polyakov action.

Citations

• Wilson Loops and Minimal Surfaces Beyond the Wavy Approximation
• Renormalized area and properly embedded minimal surfaces in hyperbolic 3-manifolds
• The dilatation operator of conformal super-Yang–Mills theory
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• The Large N Limit of Superconformal Field Theories and Supergravity

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• Wilson loops in N=4 SO(N) SYM and D-Branes in AdS₅× \mathbbRP⁵