CRITICAL BEHAVIOR IN c=1 MATRIX MODEL WITH BRANCHING INTERACTIONS

Abstract

In order to understand the phase structure of d>1 strings we investigate the c=1 matrix model with g′(tr M(t) 2 ) 2 interaction which is the simplest approximation of the large-N reduced model of odd-dimensional matrix field theory. We find three distinct phases: (i) an ordinary c=1 gravity phase, (ii) a branched polymer phase and (iii) an intermediate phase, and compute the disk and cylinder amplitudes in the phases (i) and (iii). Further we also analyze the model with slightly generalized [Formula: see text][Formula: see text] interaction. As a result the multi-critical versions of the phase (ii) are found.