Prepotential and the Seiberg-Witten Theory

الأصل · EN

Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical τ-functions, which uses as input a family of complex spectral curves with a meromorphic differential dS, subject to the constraint ∂ dS/∂(moduli)= holomorphic, and gives as an output a homogeneous prepotential on extended moduli space. Then reversed construction is discussed, which is straightforwardly generalizable from spectral curves to certain complex manifolds of dimension d >1 (like K3 and CY families). Finally, examples of particular N=2 SUSY gauge models are considered from the point of view of this formalism. At the end we discuss similarity between the WP¹²₁,₁,₂,₂,₆ -Calabi-Yau model with h₂₁=2 and the 1d SL(2) Calogero/Ruijsenaars model, but stop short of the claim that they belong to the same Whitham universality class beyond the conifold limit.