Minimal area problems and quantum open strings (Q1180369)

It is a basic combinatorial result that the Feynman rules of a field theory construct each inequivalent Feynman diagram once. For the classical closed string field theory of \textit{T. Kugo, H. Kunitomo} and \textit{K. Suehiro} [Phys. Lett. B 26, 48-54 (1989), Nucl. Phys. B 337, 434- 466 (1990)] a one-to-one correspondence between inequivalent Feynman diagrams and so-called string diagrams was established in a previous paper [the author, Commun. Math. Phys. 136, No. 1, 83-118 (1991; Zbl 0725.30032)]. A string diagram is a punctured Riemann surface (sphere in the case of classical closed string field theory) together with a choice of local analytic coordinates at the punctures. It was also proposed by the author [Mod. Phys. Lett. A 5, 2753-2762 (1990)] that a characterization of closed string diagrams by a minimal area property involving closed curves might correspond to a quantum closed string field theory. In the present paper a generalization of this definition to open- -closed string diagrams is given and it is proven that the double of such a diagram is a closed string diagram.