On the static potential in Polyakov's theory of the quantized string

We determine that part of the large-distance correction to the linear potential which is proportional to d, the number of spacetime dimensions. We find that the result depends in a surprising way on the parameter μ which appears in the Liouville theory that results when integrations over string fluctuations have been performed. For μ = 0 the correction is of the expected form $\text{≈?}\text{πd}\text{24}\text{1}\text{R}\text{, (d→?∞, R→∞)}$. However, for any μ ≠ 0 there is no 1/R potential at all with a coefficient proportional to d.