ON THE INSTANTON MODULI SPACES OF NEGATIVE DIMENSIONS
It is shown that if the contribution of flat connections on the dimension of the moduli spaces of Yang–Mills instantons and anti-instantons is appropriately taken into the account, then the inadmissible cases of negative dimensions may be reduced to zero-dimensional moduli spaces, corresponding to a collection of points, and whose counting will correspond to the Donaldson invariant of the base manifold. These results will lead to a possible description of that invariant in terms of flat connections with diverse applications, for example for testing the conjecture on its equivalence to the Seiberg–Witten invariant, and for the study of the qualitative and quantitative aspects of the gauge/gravity duality.
Using inelastic scattering of polarized neutrons near a finite Bragg reflection, the dynamics of longitudinal \ensuremath{\delta}S(q)\ensuremath{\parallel}q and transverse \ensuremath{\delta}S(q)\ensuremath{\perp}q spin fluctuations have been measured. The relaxation rates ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{\ensuremath{\alpha}}}$ follow rather precisely the dipolar dynamic-scaling function calculated recently by mode-coupling theory based on the Lorentzian approximation. The predicted longitudinal line shape near ${\mathit{T}}_{\mathit{C}}$ disagrees with our data.