Dirichlet String Theory and Singular Random Surfaces

Abstract

We show that string theory with Dirichlet boundaries is equivalent to string theory containing surfaces with certain singular points. Surface curvature is singular at these points. A singular point is resolved in conformal coordinates to a circle with Dirichlet boundary conditions. We also show that moduli parameters of singular surfaces coincide with those of smooth surfaces with boundaries. Singular surfaces with saddle points indeed arise in the strong coupling expansion in lattice QCD. The kind of saddle point, which may be the origin of a singular point we need, is of infinite order.