Exact solution of discrete two-dimensional R2 gravity Original Research Article

We exactly solve a special matrix model of dually weighted planar graphs describing pure two-dimensional quantum gravity with an R2 interaction. It permits us to study the intermediate regimes between the gravitating and flat metric. Flat space is modeled by a regular square lattice, while localised curvature is introduced through lattice defects. No “flattening” phase transition is found with respect to the R2 coupling: the infrared behaviour of the system is that of pure gravity for any finite R2 coupling. In the limit of infinite coupling, we are able to extract a scaling function interpolating between pure gravity and 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.