The Multicritical Kontsevich-Penner Model

Details The Multicritical Kontsevich-Penner Model The Multicritical Kontsevich-Penner Model

1992-01-16

arxiv.org/abs/hep-th/9201033v1

Mod.Phys.Lett. A7 (1992) 1223-1236

Physics

High Energy Physics

High Energy Physics - Theory

13 pages

Scientific paper

We consider the hermitian matrix model with an external field entering the quadratic term $\tr(\Lambda X\Lambda X)$ and Penner--like interaction term $\alpha N(\log(1+X)-X)$. An explicit solution in the leading order in $N$ is presented. The critical behaviour is given by the second derivative of the free energy in $\alpha$ which appears to be a pure logarithm, that is a feature of $c=1$ theories. Various critical regimes are possible, some of them corresponds to critical points of the usual Penner model, but there exists an infinite set of multi-critical points which differ by values of scaling dimensions of proper conformal operators. Their correlators with the puncture operator are given in genus zero by Legendre polynomials whose argument is determined by an analog of the string equation.

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