Exact Solution of Discrete Two-Dimensional R Gravity

We exactly solve a special matrix model of dually weighted planar graphs describing pure two-dimensional quantum gravity with a R interaction in order to study the intermediate regimes between the gravitating and flat metric. The flat space is modeled by a regular square lattice, while localized curvature is being introduced through defects of the lattice. No “flattening” phase transition is found with respect to the R coupling: the infrared behaviour of the system is that of pure gravity for any finite R coupling. In the limit of infinite coupling, we are able to extract a scaling function interpolating between pure gravity and a phase of a dilute gas of curvature defects on a flat background. We introduce and explain some novel techniques concerning our method of large N character expansions and the calculation of Schur characters on big Young tableaux. December 1995