CFT and topological recursion

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.

Minor corrections

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• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Invariants of spectral curves and intersection theory of moduli spaces of complex curves
• Challenges of beta-deformation
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• From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators
• A Unified Approach to Holomorphic Anomaly Equations and Quantum Spectral Curves
• Faces of matrix models
• The SYZ mirror symmetry and the BKMP remodeling conjecture
• Multi-boundary correlators in JT gravity
• Quantization of classical spectral curves via topological recursion
• A proof of loop equations in 2d topological gravity
• Analyticity of the free energy for quantum Airy structures
• Cap amplitudes in random matrix models