Abstract
We discuss how to compute connected matrix model correlators for operators related to the gravitational descendants of the puncture operator, for the topological A model on P^1. The relevant correlators are determined by recursion relations that follow from a systematic 1/N expansion of well chosen Schwinger-Dyson equations. Our results provide further compelling evidence for Gopakumar's proposed "simplest gauge string duality" between the Gaussian matrix model and the topological A model on P^1.
Highlights
Learned from such a simple example of the duality
The appendices include a discussion of the recursion relations for both the Eguchi-Yang and the Gaussian matrix models, a computation of the relevant topological string correlation functions and the computation of some matrix model correlators using orthogonal polynomials
Motivated by what may be the simplest proposal for a gauge string duality [17], we have explored the relation between correlators of the topological A model on P1 and the correlators of the Gaussian matrix model, as well as the correlators of the closely related model of Eguchi and Yang
Summary
Where M is an N × N Hermitian matrix. The correlators that participate in the duality are connected correlators of the form γ(2n1, 2n2, · · · 2nl, 2nl+1, · · · , 2nl+q) = Tr(M 2n1 ) · · · Tr(M 2nl )Tr(M 2nl+1 ln M ) · · · Tr(M 2nl+q ln M ) conn. A central observation we use is that the recursion relation of [29] can be recovered by using a systematic 1/N expansion of a suitable matrix model Schwinger-Dyson equation. The advantage of this approach is that it is simple to generalize the SchwingerDyson equation to allow for correlators that include ln M insertions. In this way, we derive a recursion relation for the general correlators γ(2n1, · · · 2nl, 2nl+1, · · · , 2nl+q) introduced above. It seems to be a highly non-trivial task to recover this recursion relation using the methods of [29]
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