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Exact Results for Topological Strings on Resolved Y p,q Singularities

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Abstract

We obtain exact results in α′ for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five dimensional gauge theories. The toric Calabi-Yaus that we analyze are obtained as minimal resolution of cones over Y p,q manifolds and give rise via M-theory compactification to SU(p) gauge theories on \({\mathbb{R}^4\times S^1}\) . As an application we present a detailed study of the local \({\mathbb{F}_2}\) case and compute open and closed genus zero Gromov-Witten invariants of the \({\mathbb{C}^3/\mathbb{Z}_4}\) orbifold. We also display the modular structure of the topological wave function and give predictions for higher genus amplitudes. The mirror curve in this case is the spectral curve of the relativistic A 1 Toda chain. Our results also indicate the existence of a wider class of relativistic integrable systems associated to generic Y p,q geometries.

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Authors and Affiliations

  1. Mathematical Physics sector, International School for Advanced Studies (SISSA/ISAS), Via Beirut 2, I-34014, Trieste, Italy

    Andrea Brini & Alessandro Tanzini

  2. Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, Trieste, Italy

    Andrea Brini & Alessandro Tanzini

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  1. Andrea Brini
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  2. Alessandro Tanzini
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Communicated by N.A. Nekrasov

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Brini, A., Tanzini, A. Exact Results for Topological Strings on Resolved Y p,q Singularities. Commun. Math. Phys. 289, 205–252 (2009). https://doi.org/10.1007/s00220-009-0814-4

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