Supersymmetric Yang-Mills, octonionic instantons and triholomorphic curves

Abstract

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this latter correspondence stems from the dynamics of various dimensional reductions of ten-dimensional supersymmetric Yang-Mills theory. More precisely we show that the dimensional reduction of the (5+1)-dimensional supersymmetric sigma model with hyperkaehler (but otherwise arbitrary) target X to a four-dimensional hyperkaehler manifold M is a topological sigma model localising on the space of triholomorphic maps M -> X (or hyperinstantons). When X is the moduli space M_K of instantons on a four-dimensional hyperkaehler manifold K, this theory has an interpretation in terms of supersymmetric gauge theory. In this case, the topological sigma model can be understood as an adiabatic limit of the dimensional reduction of ten-dimensional supersymmetric Yang-Mills on the eight-dimensional manifold M x K of holonomy Sp(1) x Sp(1) in Spin(7), which is a cohomological theory localising on the moduli space of octonionic instantons.

26 pages, LaTeX2e (A comment and a corresponding acknowledgement added and a reference ammended)

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• Higher Dimensional Analogues of Donaldson-Witten Theory
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Cited by in corpus (9)

• Superpotentials and Membrane Instantons
• Gauge theory and the division algebras
• Sigma-model limit of Yang-Mills instantons in higher dimensions
• Octonions, G_2 Symmetry, Generalized Self-Duality and Supersymmetries in Dimensions D \le 8
• Nonlinear Dirac operator and quaternionic analysis
• String theories as the adiabatic limit of Yang-Mills theory
• Analytic Loops and Gauge Fields
• Batalin--Vilkovisky quantization and supersymmetric twists
• The Ring Division Self Duality