Multi-instanton calculus versus exact results in N=2 supersymmetric QCD

TL;DR

This paper constructs multi-instanton solutions in N=2 supersymmetric SU(2) QCD and compares instanton calculus results with exact predictions, finding agreement for some cases and discrepancies for others, leading to proposed improvements.

Contribution

It provides a complete algebraic construction of super instantons in N=2 supersymmetric QCD and compares instanton calculus with exact results, highlighting discrepancies and proposing improved curves.

Findings

Instanton calculus agrees with exact results for N_f=0,1,2.

Discrepancies are found for N_f=3,4.

Proposed improved curves for N_f=3,4 theories.

Abstract

Microscopic tests of the exact results are performed in $N=2$ supersymmetric $SU(2)$ QCD. We present the complete construction of the multi-instanton in $N=2$ supersymmetric QCD. All the defining equations of the super instanton are reduced to the algebraic equations. Using this result, we calculate the two-instanton contribution ${\cal F}_2$ to the prepotential ${\cal F}$ for the arbitrary $N_f$ theories. For $N_f=0,1,2$, instanton calculus agrees with the prediction of the exact results, however, for $N_f=3,4$, we find discrepancies between them. We propose improved curves of the exact results for the massive $N_f=3$ and massless $N_f=4$ theories.