Static potential in string models

Abstract

A class of string models is studied to leading order in a $\frac{1}{d}$ expansion, where $d$ is the dimensionality of space-time. The static potential is found to be given by $V(R)={M}^{2}R{(1\ensuremath{-}\frac{{{R}_{c}}^{2}}{{R}^{2}})}^{\frac{1}{2}}$, where ${R}_{c}$ is a critical distance. At $R={R}_{c}$, the system undergoes a phase transition to a state where a quasistatic string picture is no longer applicable.