Computing topological invariants with one and two-matrix models

Abstract

A generalization of the Kontsevich Airy-model allows one to compute the intersection numbers of the moduli space of p-spin curves. These models are deduced from averages of characteristic polynomials over Gaussian ensembles of random matrices in an external matrix source. After use of a duality, and of an appropriate tuning of the source, we obtain in a double scaling limit these intersection numbers as polynomials in p. One can then take the limit p to -1 which yields a matrix model for orbifold Euler characteristics. The generalization to a time-dependent matrix model, which is equivalent to a two-matrix model, may be treated along the same lines ; it also yields a logarithmic potential with additional vertices for general p.

30 pages, added references, changed content

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Cited by in corpus (7)

• Moments of the Gaussian $\beta$ Ensembles and the large-$N$ expansion of the densities
• Duality and replicas for a unitary matrix model
• The intersection numbers of the p-spin curves from random matrix theory
• Spectral Form Factor for Time-dependent Matrix model
• Punctures and p-spin curves from matrix models II
• Punctures and p-spin curves from matrix models
• Punctures and p-spin curves from matrix models III. Dl type and logarithmic potential