A proof that Witten's open string theory gives a single cover of moduli space (Q1179854)

The author proves that the open string diagrams of Witten are unique solutions of a minimal area problem. This minimal problem asks for the metric of minimal area under the condition that all nontrivial curves with no self intersection are longer than \(\pi\). As a consequence of this result, it is proved that the Feynman diagrams of open string theory give a single cover of the moduli spaces of Riemann surfaces with \(b\geq 1\) boundaries and \(m\geq 0\) punctures.