Lattice study of area law for double-winding Wilson loops

TL;DR

This paper investigates how the area law behavior of double-winding Wilson loops in lattice SU(N) Yang-Mills theory varies with different contours and color numbers, using strong coupling expansion and Monte Carlo simulations.

Contribution

It provides a detailed analysis of the area law for double-winding Wilson loops, combining strong coupling expansion and lattice Monte Carlo methods for SU(2) and SU(3).

Findings

Area law behavior depends on the contours C1 and C2.

Strong coupling expansion matches Monte Carlo results.

Results are discussed in terms of the Non-Abelian Stokes theorem.

Abstract

We study the double-winding Wilson loops in the SU(N) Yang-Mills theory on the lattice. We discuss how the area law falloff of the double-winding Wilson loop average is modified by changing the enclosing contours C1 and C2 for various values of the number of color N. By using the strong coupling expansion, we evaluate the double-winding Wilson loop average in the lattice SU(N) Yang-Mills theory. Moreover, we compute the double-winding Wilson loop average by lattice Monte Carlo simulations for SU(2) and SU(3). We further discuss the results from the viewpoint of the Non-Abelian Stokes theorem in the higher representations.