On finite interquark potential in $D=3$ driven by a minimal length

TL;DR

This paper investigates how a quantum gravity-induced minimal length affects the interquark potential in three-dimensional Yang-Mills theory, revealing a finite interaction energy with confining behavior due to the minimal length scale.

Contribution

It introduces a novel analysis of the interquark potential incorporating a minimal length, demonstrating ultraviolet finiteness and confinement features in three-dimensional Yang-Mills.

Findings

Ultraviolet finite interaction energy obtained

Presence of a regularized logarithmic function in potential

Linear confining potential observed due to minimal length

Abstract

We address the effect of a quantum gravity induced minimal length on a physical observable for three- dimensional Yang-Mills. Our calculation is done within stationary perturbation theory. Interestingly enough, we find an ultraviolet finite interaction energy, which contains a regularized logarithmic function and a linear confining potential. This result highlights the role played by the new quantum of length in our discussion.