Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality

Abstract

We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting.

17 pages, 6 figures; references added

References in corpus (8)

• Holomorphic anomaly and matrix models
• A holomorphic and background independent partition function for matrix models and topological strings
• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
• Chern-Simons matrix models and Stieltjes-Wigert polynomials
• Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
• Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras, and their asymptotic expansions
• On Chern-Simons Matrix Models
• Introduction to the Gopakumar-Vafa Large N Duality

Cited by in corpus (13)

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• A holomorphic and background independent partition function for matrix models and topological strings
• Seiberg-Witten theory and matrix models
• Chern-Simons theory on L(p,q) lens spaces and Localization
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• Beta-ensembles for toric orbifold partition function
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• $E_8$ spectral curves
• Five-dimensional gauge theories and the local B-model
• Torus Knots in Lens Spaces & Topological Strings
• A String Dual for Partially Topological Chern-Simons-Matter Theories
• Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems
• Topological phase, spin Chern-Simons theory and level rank duality on lens space