Seiberg-Witten prepotential from instanton counting

TL;DR

This paper explores the computation of the Seiberg-Witten prepotential using instanton counting techniques, connecting physical theories with mathematical structures like moduli spaces and Young tableaux.

Contribution

It introduces a novel approach to derive the Seiberg-Witten prepotential through instanton counting, linking supersymmetric gauge theories with combinatorial identities.

Findings

Explicit computation of the Seiberg-Witten prepotential

Derivation of combinatorial identities involving Young tableaux

Connections between gauge theory and algebraic geometry

Abstract

In my lecture I consider integrals over moduli spaces of supersymmetric gauge field configurations (instantons, Higgs bundles, torsion free sheaves). The applications are twofold: physical and mathematical; they involve supersymmetric quantum mechanics of D-particles in various dimensions, direct computation of the celebrated Seiberg-Witten prepotential, sum rules for the solutions of the Bethe ansatz equations and their relation to the Laumon's nilpotent cone. As a by-product we derive some combinatoric identities involving the sums over Young tableaux.