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arXiv · 2008.03684

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

Seikou Kato·Akihiro Shibata·Kei-Ichi Kondo
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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 $N$.

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Seikou Kato, Akihiro Shibata, Kei-Ichi Kondo. 2020-08-09. Double-winding Wilson loops in SU(N) lattice Yang-Mills gauge theory. https://doi.org/10.1103/physrevd.102.094521

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