Gauge theory, calibrated geometry and harmonic spinors

Abstract

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.

20pp., exposition changed,typos corrected

References in corpus (3)

• Gauge Theory in higher dimensions, II
• Vortex equations in abelian gauged sigma-models
• J-holomorphic curves, moment maps, and invariants of Hamiltonian group actions

Cited by in corpus (19)

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• Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons
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• Sigma-model limit of Yang-Mills instantons in higher dimensions
• SU(2) solutions to self-duality equations in eight dimensions
• Deformation theory of the blown-up Seiberg-Witten equation in dimension three
• Spin(7)-instantons, Cayley submanifolds, and Fueter sections
• Generalised Seiberg-Witten equations and almost-Hermitian geometry
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• A higher dimensional foliated Donaldson theory, I
• Integrable (2k)-Dimensional Hitchin Equations
• $G_2$-instantons on noncompact $G_2$-manifolds: results and open problems
• Transversality for the moduli space of Spin(7)-instantons
• Equivariant Cerf theory and perturbative $SU(n)$ Casson invariants
• $\mathrm{Spin}(7)$-Instantons from evolution equations