CORRELATION-FUNCTIONS IN 2-DIMENSIONAL QUANTUM-GRAVITY COUPLED TO A COMPACT SCALAR FIELD

We consider the free fermion theory of the finite radius c = 1 matrix model truncated to singlet states. This truncation is expected to be exact for radius R > R(KT) because the non-singlet states implement the effects of the Kosterlitz-Thouless vortices. We calculate correlation functions of the eigenvalue density, and derive a simple general expression for finite radius correlators in terms of the non-compact ones. We give some explicit genus expansions for correlation functions of momentum operators, and obtain correlators of winding operators by the dual transformation. In conclusion, we discuss continuation to real time and physical interpretation in terms of a massless (1 + 1)-dimensional theory at finite temperature.