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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ArXiv ePrint: 1006.2028
Associate member of the Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussée, 1784 Sofia, Bulgaria. (Ivan Kostov)
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Kostov, I., Orantin, N. CFT and topological recursion. J. High Energ. Phys. 2010, 56 (2010). https://doi.org/10.1007/JHEP11(2010)056
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DOI: https://doi.org/10.1007/JHEP11(2010)056