Curvature matrix models for dynamical triangulations and the ItzyksonDi Francesco formula
Abstract
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 ItzyksonDi Francesco formula over congruence classes of Young tableau weights modulo three. From this we show that the large N limit implies a nontrivial 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 large N character expansion approach as well as potential physical applications of our results.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)00045X
 arXiv:
 arXiv:hepth/9609237
 Bibcode:
 1997NuPhB.491..689S
 Keywords:

 High Energy Physics  Theory
 EPrint:
 37 pages LaTeX