STABILIZED MATRIX MODELS FOR NONPERTURBATIVE TWO-DIMENSIONAL QUANTUM GRAVITY

Abstract

A thorough analysis of stochastically stabilized Hermitian one-matrix models for two-dimensional quantum gravity at all its (2, 2k − 1) multicritical points is made. It is stressed that only the zero fermion sector of the supersymmetric Hamiltonian, i.e. the forward Fokker–Planck Hamiltonian, is relevant for the analysis of bosonic matter coupled to two-dimensional gravity. Therefore, supersymmetry breaking is not the physical mechanism that creates nonperturbative effects in the case of points of even multicriticality k. Nonperturbative effects in the string coupling constant g str result in a loss of any explicit relation to the KdV hierarchy equations in the latter case, while maintaining the perturbative genus expansion. As a by-product of our analysis it is explicitly proved that polynomials orthogonal relative to an arbitrary weight exp (−βV (x)) along the whole real line obey a Hartree–Fock equation.