Higher Genus Correlators for the Complex Matrix Model

Details Higher Genus Correlators for the Complex Matrix Model Higher Genus Correlators for the Complex Matrix Model

1992-07-08

arxiv.org/abs/hep-th/9207020v1

Mod.Phys.Lett. A7 (1992) 3187-3202

Physics

High Energy Physics

High Energy Physics - Theory

17 pages

Scientific paper

We describe an iterative scheme which allows us to calculate any multi-loop correlator for the complex matrix model to any genus using only the first in the chain of loop equations. The method works for a completely general potential and the results contain no explicit reference to the couplings. The genus $g$ contribution to the $m$--loop correlator depends on a finite number of parameters, namely at most $4g-2+m$. We find the generating functional explicitly up to genus three. We show as well that the model is equivalent to an external field problem for the complex matrix model with a logarithmic potential.

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