MATRIX MODELS AND GAUGE-INVARIANT FIELD-THEORY OF SUBCRITICAL STRINGS

A gauge-invariant interacting field theory of subcritical closed strings is constructed. It is shown that for d less-than-or-equal-to 1 this field theory reproduces many of the features of the corresponding matrix model. Among them are the scaling dimensions of the relevant primary fields, identities involving the correlation functions of some of the redundant operators in the matrix model, and the flow between different matrix models under appropriate perturbation. In particular, it is shown that some of the constraints on the partition function derived recently by Dijkgraaf et al. and Fukuma et al. may be interpreted as Ward identities in string field theory.