2-DIMENSIONAL GRAVITY, STRING FIELD-THEORY AND SPIN-GLASSES

It is noted that an auxiliary matrix model which has appeared in recent works on non-perturbative two-dimensional gravity can be considered as a lattice version of Witten's string field theory. We consider the string field theory on a D-dimensional lattice and obtain that for the simplest interaction it is equivalent to a scalar matrix field on the lattice with local gauge invariance. We investigate the matrix model in the large N limit using the quenched prescription for D > 1 and argue the existence of a spin-glass-like phase in the string theory.