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arXiv · 1006.2028

CFT and topological recursion

Ivan Kostov·Nicolas Orantin
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Abstract

We study the quasiclassical expansion associated with a complex curve. In a more specific context this is the 1/N expansion in U(N)-invariant matrix integrals. We compare two approaches, the CFT approach and the topological recursion, and show their equivalence. The CFT approach reformulates the problem in terms of a conformal field theory on a Riemann surface, while the topological recursion is based on a recurrence equation for the observables representing symplectic invariants on the complex curve. The two approaches lead to two different graph expansions, one of which can be obtained as a partial resummation of the other.

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Ivan Kostov, Nicolas Orantin. 2010-06-10. CFT and topological recursion. https://doi.org/10.1007/jhep11(2010)056

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