Prepotential and the SeibergWitten theory
Abstract
Construction of the prepotential in the SeibergWitten theory/the Whitham hierarchy is presented. Consideration begins from the notion of quasiclassical τfunctions, which uses as an input a family of complex spectral curves with a meromorphic differential dS subject to the constraint ∂dS/ ∂(moduli) = holomorphic, and which gives as an output a homogeneous prepotential on extended moduli space. The reversed construction is then discussed, which is straightforwardly generalizable from spectral curves to certain complex manifolds of dimension d > 1 (like K3 and CY families). Examples of particular N = 2 supersymmetric gauge models are considered from the point of view of this formalism. We discuss the similarity between the WP_{1,1,2,2,6}^{12} CalabiYau model with h_{21} = 2 and the 1d SL(2) Calogero/Ruijsenaars model by deriving the respective PicardFuchs equations. We, however, stop short of the claim that they belong to the same Whitham universality class beyond the conifold limit.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(96)006797
 arXiv:
 arXiv:hepth/9512161
 Bibcode:
 1997NuPhB.491..529I
 Keywords:

 High Energy Physics  Theory
 EPrint:
 50 pages, Latex