Generalized instantons in N = 4 super Yang-Mills theory and spinorial geometry

Abstract

Using spinorial geometry techniques, we classify the supersymmetric solutions of euclidean $\mathcal{N}=4$ super Yang-Mills theory. These backgrounds represent generalizations of instantons with nontrivial scalar fields turned on, and satisfy some constraints that bear a similarity with the Hitchin equations, and contain the Donaldson equations as a special subcase. It turns out that these constraints can be obtained by dimensional reduction of the octonionic instanton equations, and may be rephrased in terms of a selfduality-like condition for a complex connection. We also show that the supersymmetry conditions imply the equations of motion only partially.

29 pages, 3 tables. v2: references added. v3: conclusion extended, version published in JHEP

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• Euclidean N=2 Supergravity
• SU(2) solutions to self-duality equations in eight dimensions
• Para-Complex Geometry and Gravitational Instantons
• On supersymmetric Einstein-Weyl spaces
• On Finite-Size D-Branes in Superstring Theory