L. Bonora et Cs. Xiong, EXTENDED TODA LATTICE HIERARCHY, EXTENDED 2-MATRIX MODEL AND C=1 STRING THEORY, Nuclear physics. B, 434(1-2), 1995, pp. 408-444
We show how the two-matrix model and Toda lattice hierarchy presented
in a previous paper can be solved exactly: we obtain compact formulas
for correlators of pure tachyonic states at every genus. We then exten
d the model to incorporate a set of discrete states organized in finit
e dimensional sl(2) representations. We solve also this extended model
and find the correlators of the discrete states by means of the W con
straints and the flow equations. Our results coincide with the ones ex
isting in the literature in those cases in which particular correlator
s have been explicitly calculated. We conclude that the extended two-m
atrix model is a realization of the discrete states of c = 1 string th
eory.