On an Airy matrix model with a logarithmic potential

Details On an Airy matrix model with a logarithmic potential On an Airy matrix model with a logarithmic potential

2011-08-09

arxiv.org/abs/1108.1958v1

Physics

Mathematical Physics

35 pages

Scientific paper

The Kontsevich-Penner model, an Airy matrix model with a logarithmic potential, may be derived from a simple Gaussian two-matrix model through a duality. In this dual version the Fourier transforms of the n-point correlation functions can be computed in closed form. Using Virasoro constraints, we find that in addition to the parameters $t_n$, which appears in the KdV hierarchies, one needs to introduce here half-integer indices $t_{n/2}$ . The free energy as a function of those parameters may be obtained from these Virasoro constraints. The large N limit follows from the solution to an integral equation. This leads to explicit computations for a number of topological invariants.

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