Comparing Instanton Contributions with Exact Results in N=2 Supersymmetric Scale Invariant Theories

TL;DR

This paper compares instanton calculations with exact results in N=2 supersymmetric QCD, resolving previous discrepancies and confirming agreement in low-energy effective couplings for SU(N) theories with fundamental hypermultiplets.

Contribution

It clarifies the matching process between instanton methods and exact results in scale-invariant N=2 supersymmetric theories, resolving prior disagreements.

Findings

Confirmed agreement of low-energy couplings for SU(N) with 2N hypermultiplets

Resolved ambiguities in matching instanton and exact results

Verified results at a special Coulomb branch vacuum

Abstract

We discuss the general issues and ambiguities involved in matching the exact results for the low energy effective action of scale invariant N=2 supersymmetric QCD to those obtained by instanton methods. We resolve the reported disagreements and verify agreement between an infinite series of coefficients in the low energy effective actions calculated in the two approaches. In particular, we show that the exact low-energy effective couplings for SU(N) for all N with 2N fundamental hypermultiplets agree at a special vacuum on the Coulomb branch where a large unbroken discrete global symmetry makes the matching of parameters relatively straightforward.