Minimal Area Nonorientable String Diagrams

We use minimal area metrics to generate all nonorientable string diagrams. The surfaces in unoriented string theory have nontrivial open curves and nontrivial closed curves whose neighborhoods are either annuli or Möbius strips. We define a minimal area problem by imposing length conditions on open curves and on annular closed curves only. We verify that the minimal area conditions are respected by the sewing operations. The natural objects that satisfy recursion relations involving the propagator, which performs both orientable and nonorientable sewing, are classes of moduli spaces grouped by Euler characteristic. email: [email protected] Work supported by the U.S. Department of Energy under contract #DE-FC02-94ER40818.