Gauge Theory in higher dimensions, II

Abstract

The main aim of the paper is to develop the "Floer theory" associated to Calabi-Yau 3-folds, exending the analogy of Thomas' "holomorphic Casson invariant". The treatment in the body of the paper is largely formal, assuming appropriate compactness properties of moduli spaces of $G_2$-instantons, but in the last section we make some remarks about these compactness isssues. Section 3 of the paper contains a general dscussion of deformations of the equations, for gauge field and submanifolds, associated to manifolds with exceptional holonomy.

References in corpus (2)

• Gauge theory, calibrated geometry and harmonic spinors
• Lefschetz fibrations, intersection numbers, and representations of the framed braid group

Cited by in corpus (32)

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• Brane Effective Actions, Kappa-Symmetry and Applications
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• Fukaya-Seidel category and gauge theory
• Gauge theory, calibrated geometry and harmonic spinors
• Yang-Mills instantons and dyons on homogeneous G_2-manifolds
• The infinitesimal moduli space of heterotic $G_2$ systems
• Monopoles on the Bryant-Salamon $G_2$ Manifolds
• On orientations for gauge-theoretic moduli spaces
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Contact Manifolds, Contact Instantons, and Twistor Geometry
• Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons
• Deformations of associative submanifolds with boundary
• A construction of Spin(7)-instantons
• Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons
• Sigma-model limit of Yang-Mills instantons in higher dimensions
• Canonical orientations for moduli spaces of $G_2$-instantons with gauge group SU(m) or U(m)
• Conjectures on counting associative 3-folds in $G_2$-manifolds
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• Deformations of Asymptotically Conical $G_2$-Instantons
• Counting Associatives in Compact $G_2$ Orbifolds
• Note on a Cohomological Theory of Contact-Instanton and Invariants of Contact Structures
• Holography for field theory solitons
• On the Moyal deformation of Nahm Equations in seven dimensions
• Asymptotic behaviour of instantons on Cylinder Manifolds
• A formally Kahler structure on a knot space of a G2-manifold
• Local Nahm transform and singularity formation of ASD connections
• Stable Yang-Mills connections on Special Holonomy Manifolds
• Instantons on Cylindrical Manifolds
• Yang-Mills connections on $G_2$-manifolds and Calabi-Yau 3-folds
• $L^2$ harmonic forms on complete special holonomy manifolds
• Families of solutions of the heterotic G${}_2$ system