Gauge theory, calibrated geometry and harmonic spinors

Understand

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.