2006/07/21 by Diaconescu, Duiliu-Emanuel, Donagi, Ron, Pantev, Tony
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.hep-th/0607159
Let Σ be a smooth projective complex curve and \mathfrakg a simple Lie algebra of type \sf ADE with associated adjoint group G. For a fixed pair (Σ, \mathfrakg), we construct a family of quasi-projective Calabi-Yau threefolds parameterized by the base of the Hitchin integrable system associated to (Σ,\mathfrakg). Our main result establishes an isomorphism between the Calabi-Yau integrable system, whose fibers are the intermediate Jacobians of this family of Calabi-Yau threefolds, and the Hitchin system for G, whose fibers are Prym varieties of the corresponding spectral covers. This construction provides a geometric framework for Dijkgraaf-Vafa transitions of type \sf ADE. In particular, it predicts an interesting connection between adjoint \sf ADE Hitchin systems and quantization of holomorphic branes on Calabi-Yau manifolds.