  The unitarity problem in curved spacetime is solved for the string described
by the SL(2,R) WZW model. The spectrum is computed exactly and demonstratedto
be ghost-free. The new features include (i) SL(2,R) left/right symmetrycurrents
that have logarithmic cuts on the world sheet but that satisfy theusual local
operator products or commutation rules, (ii) physical statesconsistent with the
monodromy condition of closed strings despite thelogarithmic singularity in the
currents, and (iii) a new free boson realization for these currents which
render the SL(2,R) WZW model completely solvable.
