Gauge zero modes, instanton determinants, and quantum-chromodynamic calculations

Abstract

A treatment of the gauge zero modes about an instanton in a singular gauge places them on the same footing as all other zero modes and simplifies the calculation of the collective-coordinate part of the instanton determinant. This determinant is calculated first for the gauge group SU(3) and then for general $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$. The answers differ from previously published results: For SU(3), the reason for this difference is trivial [the inclusion of certain factors of $\frac{1}{\sqrt{2}}$ whose absence from 't Hooft's original SU(2) calculation was recently discovered] but the effects on quantum-chromodynamic calculations may be important; for large $N$, the reasons are more involved, but the usual conclusion that instantons are absent in the planar limit is unaffected.