Multi-Instanton Calculus in N=2 Supersymmetric Gauge Theory II: Coupling to Matter

TL;DR

This paper extends the analysis of N=2 superinstantons in SU(2) gauge theory by including matter hypermultiplets, providing explicit instanton calculations that confirm Seiberg-Witten predictions with some finite renormalizations.

Contribution

It introduces a superfield formalism for N=2 superinstantons with matter, enabling precise instanton calculations and revealing finite renormalizations for N_F=4.

Findings

Explicit 1- and 2-instanton checks match Seiberg-Witten predictions

Inclusion of hypermultiplets in superinstanton calculus

Finite renormalization of coupling for N_F=4

Abstract

We further discuss the N=2 superinstantons in SU(2) gauge theory, obtained from the general self-dual solutions of topological charge n constructed by Atiyah, Drinfeld, Hitchin and Manin (ADHM). We realize the N=2 supersymmetry algebra as actions on the superinstanton moduli. This allows us to recast in concise superfield notation our previously obtained expression for the exact classical interaction between n ADHM superinstantons mediated by the adjoint Higgs bosons, and moreover, to incorporate N_F flavors of hypermultiplets. We perform explicit 1- and 2-instanton checks of the Seiberg-Witten prepotentials for all N_F and arbitrary hypermultiplet masses. Our results for the low-energy couplings are all in precise agreement with the predictions of Seiberg and Witten except for N_F=4, where we find a finite renormalization of the coupling which is absent in the proposed solution.