Exact results for topological strings on resolved y p,q singularities

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Colleges, School and Institutes

External organisations

  • Mathematical Physics sector, International School for Advanced Studies (SISSA/ISAS)
  • Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste


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 ℝ4× S1. As an application we present a detailed study of the local F2case and compute open and closed genus zero Gromov-Witten invariants of the bC3Z4 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.


Original languageEnglish
Pages (from-to)205-252
Number of pages48
JournalCommunications in Mathematical Physics
Issue number1
Early online date24 Apr 2009
Publication statusPublished - 1 Jul 2009


  • Gauge Theory, Modulus Space, Modular Form, Topological String, Toda Chain