  In this paper connections between different gauge-theoretical problems in
high and low dimensions are established. In particular it is shown that higher
dimensional asd equations on total spaces of spinor bundles over low
dimensional manifolds can be interpreted as Taubes-Pidstrygach's generalization
of the Seiberg-Witten equations. By collapsing each fibre of the spinor bundle
to a point, solutions of the Taubes-Pidstrygach equations are related to
generalized harmonic spinors. This approach is also generalized for arbitrary
fibrations (without singular fibres) compatible with an appropriate
calibration.
