Curve counting and instanton counting

Abstract

We prove some combinatorial results required for the proof of the following conjecture of Nekrasov: The generating function of closed string invariants in local Calabi-Yau geometries obtained by appropriate fibrations of $A_N$ singularities over $P^1$ reproduce the generating function of equivariant $\hat{A}$-genera of moduli space of instants on $C^2$.

References in corpus (4)

• Geometric Engineering of Quantum Field Theories
• Hodge integrals, Hurwitz numbers, and Symmetric Groups
• A Conjecture on Hodge Integrals
• Localizations on Moduli Spaces and Free Field Realizations of Feynman Rules

Cited by in corpus (19)

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• Geometric transitions, Chern-Simons gauge theory and Veneziano type amplitudes
• A Combinatorial Study on Quiver Varieties
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Crepant resolution conjecture in all genera for type A singularities
• Formulae of one-partition and two-partition Hodge integrals
• Open String Invariants and Mirror Curve of the Resolved Conifold
• A simple proof of Gopakumar-Vafa conjecture for local toric Calabi-Yau manifolds
• Instanton Counting and Dielectric Branes
• K-Theory of Hilbert Schemes as a Formal Quantum Field Theory
• On fermionic representation of the framed topological vertex
• Asymptotic Form of Gopakumar-Vafa Invariants from Instanton Counting
• Towards a gauge theory interpretation of the real topological string
• Affine SU(N) algebra from wall-crossings
• On fermionic representation of the Gromov-Witten invariants of the resolved Conifold
• A Proof of the Full Marino-Vafa Conjecture