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SU(N) Geometries and Topological String Amplitudes

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arxiv hep-th/0306032 v2 pith:UT3RWMFI submitted 2003-06-04 hep-th

SU(N) Geometries and Topological String Amplitudes

classification hep-th
keywords theoryfieldfunctionsgaugegeometricgeometrieslimitpartition
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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It has been conjectured recently that the field theory limit of the topological string partition functions, including all higher genus contributions, for the family of CY3-folds giving rise to N=2 4D SU(N) gauge theory via geometric engineering can be obtained from gauge instanton calculus. We verify this surprising conjecture by calculating the partition functions for such local CYs using diagrammatic techniques inspired by geometric transitions. Determining the Gopakumar-Vafa invariants for these geometries to all orders in the fiber wrappings allows us to take the field theory limit.

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Cited by 1 Pith paper

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    hep-th 2025-11 conditional novelty 7.0

    Explicit entire eigenfunctions are constructed for the difference operators 2Λ^N cosh(p)+V_N(x) with arbitrary polynomial potential; they become square-integrable only at a discrete set of energies.