An Algorithm for the Microscopic Evaluation of the Coefficients of the Seiberg-Witten Prepotential

TL;DR

This work develops a practical algorithm to compute Seiberg–Witten prepotential coefficients from microscopic instanton data in N=2 SU(2) Yang–Mills theory by employing a non-commutative deformation to regularize the instanton moduli space and a modified vector-field localization. The method reduces the path integrals to finite sums over fixed points labeled by pairs of Young diagrams, and the authors present explicit 1–4 instanton results, supported by a general determinant formula for SU(N) that extends to higher instanton numbers. They connect the generating function of instanton contributions (Nekrasov partition function) to the prepotential coefficients through the ε1, ε2 -> 0 limit, offering a concrete route to verify Seiberg–Witten predictions from first-principles calculations. The framework combines ADHM data, equivariant localization, and Young diagram combinatorics to enable systematic, high-precision computations of nonperturbative contributions in supersymmetric gauge theories.

Abstract

A procedure, allowing to calculate the coefficients of the SW prepotential in the framework of the instanton calculus is presented. As a demonstration explicit calculations for 2, 3 and 4- instanton contributions are carried out.