English

The coefficients of the Seiberg-Witten prepotential as intersection numbers (?)

High Energy Physics - Theory 2007-05-23 v1 Algebraic Geometry

Abstract

The nn-instanton contribution to the Seiberg-Witten prepotential of N=2{\bf N}=2 supersymmetric d=4d=4 Yang Mills theory is represented as the integral of the exponential of an equivariantly exact form. Integrating out an overall scale and a U(1) angle the integral is rewritten as (4n3)(4n-3) fold product of a closed two form. This two form is, formally, a representative of the Euler class of the Instanton moduli space viewed as a principal U(1) bundle, because its pullback under bundel projection is the exterior derivative of an angular one-form. We comment on a recent speculation of Matone concerning an analogy linking the instanton problem and classical Liouville theory of punctured Riemann spheres.

Keywords

Cite

@article{arxiv.hep-th/0110240,
  title  = {The coefficients of the Seiberg-Witten prepotential as intersection numbers (?)},
  author = {R. Flume and R. Poghossian and H. Storch},
  journal= {arXiv preprint arXiv:hep-th/0110240},
  year   = {2007}
}

Comments

21 pages, To be published in the collection ``From Integrable Models to Gauge Theories'' (World Scientific, Singapore, 02) to honour Sergei Matinyan at the occasion of his 70'th birthday