Almost Flat Planar Diagrams

Details Almost Flat Planar Diagrams Almost Flat Planar Diagrams

1995-06-27

arxiv.org/abs/hep-th/9506174v1

Commun.Math.Phys. 179 (1996) 235-256

Physics

High Energy Physics

High Energy Physics - Theory

harvmac.tex and pictex.tex. Must be compiled "big". Diagrams are written directly into the text in pictex commands

Scientific paper

10.1007/BF02103721

We continue our study of matrix models of dually weighted graphs. Among the attractive features of these models is the possibility to interpolate between ensembles of regular and random two-dimensional lattices, relevant for the study of the crossover from two-dimensional flat space to two-dimensional quantum gravity. We further develop the formalism of large $N$ character expansions. In particular, a general method for determining the large $N$ limit of a character is derived. This method, aside from being potentially useful for a far greater class of problems, allows us to exactly solve the matrix models of dually weighted graphs, reducing them to a well-posed Cauchy-Riemann problem. The power of the method is illustrated by explicitly solving a new model in which only positive curvature defects are permitted on the surface, an arbitrary amount of negative curvature being introduced at a single insertion.

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