Exactly solvable field theories of closed strings

Field theories of closed strings are shown to be exactly solvable for a central charge of matter fields c=1-6/m(m+1), m=1, 2, 3,.... The two-point function χ(λ,N), in which λ is the cosmological constant and N-1 is the string coupling constant, obeys a scaling law χ(λ,N)=N-(m+1/2)f((λc-λ)Nm/(m+1/2)) in the limit in which N-1 goes to zero and λ goes to a critical value λc; we have determined the universal non-linear differential equation satisfied by the function f. From this equation it is found that a phase transition takes place for some finite value of the scaling parameter (λc-λ)Nm/(m+1/2); this transition is a ''condensation of handles'' on the world sheet, characterized by a divergence of the averaged genus of the world sheets. The cases m=2,3 are elaborated in more details, and the case m=1, which corresponds to the embedding of a bosonic string in -2 dimensions, is reduced to explicit quadratures. (orig.)