One-Instanton Tests of the Exact Results in N=2 Supersymmetric QCD

TL;DR

This paper uses instanton calculus to test and refine the exact solutions of N=2 supersymmetric QCD, revealing discrepancies and improving curve parameterizations for certain flavor numbers.

Contribution

It provides the first microscopic instanton calculation of specific quantum moduli and uses these results to evaluate and improve the hyperelliptic curve predictions in N=2 SQCD.

Findings

Agreement with curve predictions up to regular terms for N_f<2N_c

Disagreement with all suggested curves for SU(3) at N_f=3

Refinement of curve parameterization based on instanton results

Abstract

We use the microscopic instanton calculus to determine the one-instanton contribution to the quantum modulus u_3=<Tr(\phi^3)> in N=2 SU(N_c) supersymmetric QCD with N_f<2N_c fundamental flavors. This is compared with the corresponding prediction of the hyperelliptic curves which are expected to give exact solutions in this theory. The results agree up to certain regular terms which appear when N_f\geq 2N_c-3. The curve prediction for these terms depends upon the curve parameterization which is generically ambiguous when N_f\geq N_c. In SU(3) theory our instanton calculation of the regular terms is found to disagree with the predictions of all of the suggested curves. For this theory we employ our results as input to improve the curve parameterization for N_f=3,4,5.