Polyakov bosonic string and the properies of its mesure

Abstract

The analytic properties of Polyakov bosonic string measure are studied as function of the complex coordinates on Moduli space $M_p$. It is seen that the measure multiplied by $(\det\; \mbox{Im} \tilde{\tau})^{13}$ (where $\tilde{\tau}$ is the period matrix of the Riemann surface) is the absolute square of a function holomorphic and no where vanishing on $M_p$ and the function has a second-order pole at the boundary $D=\overline{M}_p/M_p$.