Dirichlet Boundary Conditions in Generalized Liouville Theory toward a   QCD String
  We consider bosonic noncritical strings as QCD strings and we present a basic strategy to construct them in the context of Liouville theory. We show that Dirichlet boundary conditions play important roles in generalized Liouville theory. Specifically, they are used to stabilize the classical configuration of strings and also utilized to treat tachyon condensation in our model. We point out that Dirichlet boundary conditions for the Liouville mode maintains Weyl invariance, if an appropriate condition is satisfied, in the background with a (non-linear) dilaton. 
Shin Nakamura