Exact solution of the O( n) model on a random lattice
Abstract
We present an exact solution of the O( n) model on a random lattice. The coupling constant space of our model is parametrized in terms of a set of moment variables and the same type of universality with respect to the potential as observed for the onematrix model is found. In addition we find a large degree of universality with respect to n; namely for ngE ]  2,2[ the solution can be presented in a form which is valid not only for any potential, but also for any n (not necessarily rational). The cases n = ±2 are treated separately. We give explicit expressions for the genuszero contribution to the one and twoloop correlators as well as for the genusone contribution to the oneloop correlator and the free energy. It is shown how one can obtain from these results any multiloop correlator and the free energy to any genus and the structure of the highergenera contributions is described. Furthermore we describe how the calculation of the highergenera contributions can be pursued in the scaling limit.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1995
 DOI:
 10.1016/05503213(95)004699
 arXiv:
 arXiv:hepth/9506193
 Bibcode:
 1995NuPhB.455..577E
 Keywords:

 High Energy Physics  Theory
 EPrint:
 44 pages, LaTeX file, no figures