Generalized quark-antiquark potential at weak and strong coupling

TL;DR

This paper investigates a two-parameter family of Wilson loops in N=4 SYM theory, bridging known configurations, and computes their behavior at weak and strong coupling, providing insights into the generalized quark-antiquark potential.

Contribution

It introduces a new two-parameter family of Wilson loops and computes their expectation values at both weak and strong coupling regimes, extending previous understanding of quark-antiquark potentials.

Findings

Computed Wilson loops to second order in perturbation theory.

Performed semiclassical string theory calculations to one-loop order.

Provided integral forms for the determinants and discussed all-loop potential derivations.

Abstract

We study a two-parameter family of Wilson loop operators in N=4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. We calculate these loops on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. We comment about the feasibility of deriving all-loop results for these Wilson loops.