On an Airy matrix model with a logarithmic potential

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 the closed form. Using Virasoro constraints,...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-02, Vol.45 (4), p.45203-26
Main Authors: Brézin, E, Hikami, S
Format: Article
Language:English
Subjects:
Computation
Exact sciences and technology
Exact solutions
Fourier transforms
Free energy
Gaussian
Hierarchies
integrable hierarchies
Invariants
Mathematical analysis
Mathematical models
matrix models
Physics
topological field theory
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Summary: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 the closed form. Using Virasoro constraints, we find that in addition to the parameters tn, which appear in the Korteweg-de Vries hierarchies, one needs to introduce half-integer indices tn 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.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/4/045203