Correlation Functions of Complex Matrix Models

• Main Author: Bergère, M. C
• Format: Journal Article
• Language: English
• Published: 02.11.2005
• Subjects: Physics - High Energy Physics - Theory
• DOI: 10.48550/arxiv.hep-th/0511019

J.Phys.A39:8749-8774,2006 For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is function of four kernels constructed from the orthogonal polynomials corresponding to the potential and from their Cauchy transform. The correlation functions are a sum of expressions attached to a set of fully packed oriented loops configurations; for rotational invariant systems, explicit expressions can be written for each configuration and more specifically for the Gaussian potential, we obtain the large $N$ expansion ('t Hooft expansion) and the so-called BMN limit.