Computing topological invariants with one and two-matrix models

Details Computing topological invariants with one and two-matrix models Computing topological invariants with one and two-matrix models

2008-10-07

arxiv.org/abs/0810.1085v2

JHEP 0904:110,2009

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, added references, changed content

Scientific paper

10.1088/1126-6708/2009/04/110

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.

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