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

Abstract

The $n$-instanton contribution to the Seiberg-Witten prepotential of $\mathbf{N}=2$ supersymmetric $d=4$ 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 $(4n-3)$ 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.

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