$R^2$ 2D Quantum Gravity and Dually Weighted Graphs

Details $R^2$ 2D Quantum Gravity and Dually Weighted Graphs $R^2$ 2D Quantum Gravity and Dually Weighted Graphs

1996-05-14

arxiv.org/abs/hep-th/9605098v1

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LATEX, uses sprocl.sty; Talk based on a recent paper of M.Staudacher, T.Wynter and myself and presented on the Confe

Scientific paper

A recently introduced model of dually weighted planar graphs is solved in terms of an elliptic parametrization for some particular collection of planar graphs describing the 2D $R^2$ quantum gravity. Along with the cosmological constant $\lambda$ one has a coupling $\beta$ in the model corresponding to the $R^2$-coupling constant. It is shown that for any value of $\beta$ the large scale behavior of the model corresponds to that of the standard pure 2D quantum gravity. On small distances it describes the dynamics of point-like curvature defects introduced into the flat 2D space. The scaling function in the vicinity of almost flat metric is obtained. The major steps of the exact solution are given.

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