NONCRITICAL OPEN STRINGS BEYOND THE SEMICLASSICAL APPROXIMATION

We studied the lowest order quantum corrections to the macroscopic wav e functions Gamma(A,l) of non-critical string theory using the semicla ssical expansion of Liouville theory. By carefully taking the perimete r constraint into account we obtained a new type of boundary condition for the Liouville field which is compatible with the reparametrizatio n invariance of the boundary and which is not only a mixture of Dirich let and Neumann types but also involves an integral of an exponential of the Liouville field along the boundary. This condition contains an unknown function of A/l(2). We determined this function by computing p art of the one-loop corrections to Gamma(A,l).