Spontaneous Generation of String Tension and Quark Potential

The quark potential of a string with extrinsic curvature is calculated in the limit $d\to \infty$, via a saddlepoint approximation. The saddle point has an anisotropic gap matrix ${\lambda }^{\mathrm{ij}}$ ($\ne \lambda g^{\mathrm{ij}}$ in contrast to an unjustified assumption in all previous discussions). The anisotropy enters the nonleading $-\frac{\mathrm{}(d-2\mathrm{})\mathrm{}\pi c}{24R}$ part of the potential. $c$ is calculated, the entire potential is plotted, and simple analytic expressions are found which approximate all quantities involved very closely.