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arXiv · 0906.0036

Exact 2-point function in Hermitian matrix model

A. Morozov·Sh. Shakirov
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Abstract

J. Harer and D. Zagier have found a strikingly simple generating function for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.

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A. Morozov, Sh. Shakirov. 2009-06-01. Exact 2-point function in Hermitian matrix model. https://doi.org/10.1088/1126-6708/2009/12/003

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