2008/04/30 by Andrea Brini, Alessandro Tanzini · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Compactification (mathematics) #Gauge theory #Genus #Geometric and Algebraic Topology #Geometry and complex manifolds #Gravitational singularity #Integrable system #Minimal models #Toda lattice #Topological string theory #Topology (electrical circuits) #hep-th #math-ph #math.AG #math.MP
paper · pdf · doi:10.1007/s00220-009-0814-4
published as Commun.Math.Phys.289:205-252,2009 · 54 pages, 10 figures; typos corrected, new section added. Version accepted for publication on Communications in Mathematical Physics
arxiv created 2009/02/26 · openalex publication_date 2009/04/23 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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-Yau's 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 x S1. As an application we present a detailed study of the local F2 case and compute open and closed genus zero Gromov-Witten invariants of the C3/Z4 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 A1 Toda chain. Our results also indicate the existence of a wider class of relativistic integrable systems associated to generic Y(p,q) geometries.