Non-Critical Open Strings Beyond the Semiclassical Approximation

Abstract

We studied the lowest order quantum corrections to the macroscopic wave functions Γ(A,ℓ) of non-critical string theory using the semiclassical expansion of Liouville theory. By carefully taking the perimeter constraint into account we obtained a new type of boundary condition for the Liouville field which is compatible with the reparametrization invariance of the boundary and which is not only a mixture of Dirichlet 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/ℓ2. We determined this function by computing part of the one-loop corrections to Γ(A,ℓ).