Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-09-30
Nucl.Phys. B491 (1997) 689-723
Physics
High Energy Physics
High Energy Physics - Theory
37 pages LaTeX; Some clarifying comments added, last Section rewritten
Scientific paper
10.1016/S0550-3213(97)00045-X
We study the large-N limit of a class of matrix models for dually weighted triangulated random surfaces using character expansion techniques. We show that for various choices of the weights of vertices of the dynamical triangulation the model can be solved by resumming the Itzykson-Di Francesco formula over congruence classes of Young tableau weights modulo three. From this we show that the large-N limit implies a non-trivial correspondence with models of random surfaces weighted with only even coordination number vertices. We examine the critical behaviour and evaluation of observables and discuss their interrelationships in all models. We obtain explicit solutions of the model for simple choices of vertex weightings and use them to show how the matrix model reproduces features of the random surface sum. We also discuss some general properties of the large-N character expansion approach as well as potential physical applications of our results.
Szabo Richard J.
Wheater John F.
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