Vertices from replica in a random matrix theory

Abstract

Kontsevitch's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In a subsequent work Okounkov rederived these results from the edge behavior of a Gaussian matrix integral. In our work we consider the correlation functions of vertices in a Gaussian random matrix theory, with an external matrix source, in a scaling limit in which the powers of the matrices and their sizes go to infinity simultaneously in a specified scale. We show that the replica method applied to characteristic polynomials of the random matrices, together with a duality exchanging N and the number of points, allows one to recover Kontsevich's results on the intersection numbers, through a simple saddle-point analysis.

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Cited by in corpus (16)

• Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Octagons I: Combinatorics and Non-Planar Resummations
• Intersection theory from duality and replica
• Absorption of closed strings by giant gravitons
• Differential identities for the structure function of some random matrix ensembles
• The n-point functions for intersection numbers on moduli spaces of curves
• On an Airy matrix model with a logarithmic potential
• The intersection numbers of the p-spin curves from random matrix theory
• Gravity without averaging
• Descendent integrals and tautological rings of moduli spaces of curves
• Note on a duality of topological branes
• Buryak-Okounkov formula for the $n$-point function and a new proof of the Witten conjecture
• Superintegrability and Kontsevich-Hermitian relation
• Random Matrix, Singularities and Open/Close Intersection Numbers
• New properties of the intersection numbers on moduli spaces of curves