Exact Solution of Discrete Two-Dimensional R^2 Gravity

Details Exact Solution of Discrete Two-Dimensional R^2 Gravity Exact Solution of Discrete Two-Dimensional R^2 Gravity

1996-01-14

arxiv.org/abs/hep-th/9601069v3

Nucl.Phys. B471 (1996) 309-333

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 6 ps figures, uses harvmac.tex and epsf, minor changes

Scientific paper

10.1016/0550-3213(96)00184-8

We exactly solve a special matrix model of dually weighted planar graphs describing pure two-dimensional quantum gravity with an R^2 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 R^2 coupling: the infrared behaviour of the system is that of pure gravity for any finite R^2 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.

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