Double-winding Wilson loops in SU(N) lattice Yang-Mills gauge theory

TL;DR

This paper investigates the behavior of double-winding Wilson loops in SU(N) lattice Yang-Mills theory, revealing different area law falloffs depending on N and the spatial configuration of the loops through both analytical and numerical methods.

Contribution

It introduces a detailed analysis of double-winding Wilson loops, identifying novel area law behaviors and their dependence on the number of colors and loop configurations.

Findings

Coplanar double-winding loops obey max-of-areas law for N=3.

Sum-of-areas law applies for N≥4.

Long-distance behavior of shifted loops is N-independent, short-distance behavior depends on N.

Abstract

We study double-winding Wilson loops in $SU(N)$ lattice Yang-Mills gauge theory by using both strong coupling expansions and numerical simulations. First, we examine how the area law falloff of a ``coplanar'' double-winding Wilson loop average depends on the number of color $N$. Indeed, we find that a coplanar double-winding Wilson loop average obeys a novel ``max-of-areas law'' for $N=3$ and the sum-of-areas law for $N\geq 4$, although we reconfirm the difference-of-areas law for $N=2$. Second, we examine a ``shifted'' double-winding Wilson loop, where the two constituent loops are displaced from one another in a transverse direction. We evaluate its average by changing the distance of a transverse direction and we find that the long distance behavior does not depend on the number of color $N$, while the short distance behavior depends strongly on $N$.