Testing the self-duality of topological lumps in SU(3) lattice gauge theory

We discuss a simple formula which connects the field-strength tensor to a spectral sum over certain quadratic forms of the eigenvectors of the lattice Dirac operator. We analyze these terms for the near zero modes and find that they give rise to contributions which are essentially either self-dual or anti-self-dual. Modes with larger eigenvalues in the bulk of the spectrum are more dominated by quantum fluctuations and are less (anti-)self-dual. In the high temperature phase of QCD we find considerably reduced (anti-)self-duality for the modes near the edge of the spectral gap.