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