A NAIVE MATRIX-MODEL APPROACH TO 2D QUANTUM-GRAVITY COUPLED TO MATTER OF ARBITRARY CENTRAL CHARGE

In the usual matrix-model approach to random discretized two-dimensional manifolds, one introduces n Ising spins on each cell. i.e., a discrete version of 2D quantum gravity coupled to matter with a central charge 1/2n. The matrix model consists then of an integral over 2n matrices, which we are unable to solve for n > 1. However. for a fixed genus we can expand in the cosmological constant g for arbitrary values of n, and a simple minded analysis of the series yields for n = 0, 1 and 2 the expected results for the exponent gamma(string) with an amazing precision given the small number of terms that we considered. We then proceed to larger values of n. Simple tests of universality are successfully applied; for instance. we obtain the same exponents for n = 3 or for the one-Ising model coupled to a one-dimensional target space. The calculations are easily extended to q-states Potts models, through an integration over q(n) matrices. We see no sign of the tachyonic instability of the theory, but we have only considered genus zero at this stage.