INTEGRABILITY OF SCHWINGER-DYSON EQUATIONS IN 2D QUANTUM-GRAVITY AND C-LESS-THAN-1 NONCRITICAL STRING FIELD-THEORY

We investigate the integrability of the Schwinger-Dyson equations in c = 1 - 6/m(m+1) string field theory which were proposed by Ikehara et al. as the continuum limit of the Schwinger-Dyson equations of the matrix chain model. We show the continuum Schwinger-Dyson equations generate a closed algebra. This algebra contains Virasoro algebra but does nor coincide with W-infinity algebra. We include in the Schwinger-Dyson equations a new process of removing from the loop boundaries the operator H(sigma) which locally changes the spin configuration We also derive the string field Hamiltonian from the continuum Schwinger-Dyson equations. Its form is universal for all c = 1 - 6/m(m+1) string theories.