Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-12-10
Int.J.Mod.Phys. A9 (1994) 3751-3772
Physics
High Energy Physics
High Energy Physics - Theory
31pp,latex, TECHNION-PH-35
Scientific paper
10.1142/S0217751X94001503
A thorough analysis of stochastically stabilised 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 non perturbative effects in the case of points of even multicriticality $k$. Non perturbative 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 $\exp (-\beta V(x))$ along the whole real line obey an Hartree-Fock equation.
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