Super self-duality for Yang-Mills fields in dimensions greater than four

TL;DR

This paper explores super self-duality equations for Yang-Mills fields in higher dimensions, extending classical self-duality concepts to superspace and providing a systematic group-theoretic approach with concrete examples.

Contribution

It introduces a novel group theory-based algorithm to find super self-duality systems in various dimensions, including Spin(7) and G(2) invariant cases.

Findings

Developed a systematic method for super self-duality equations.

Provided explicit examples in 7 and 8 dimensions.

Extended classical self-duality to superspace contexts.

Abstract

Self-duality equations for Yang-Mills fields in d-dimensional Euclidean spaces consist of linear algebraic relations amongst the components of the curvature tensor which imply the Yang-Mills equations. For the extension to superspace gauge fields, the super self-duality equations are investigated, namely, systems of linear algebraic relations on the components of the supercurvature, which imply the self-duality equations on the even part of superspace. A group theory based algorithm for finding such systems is developed. Representative examples in various dimensions are provided, including the Spin(7) and G(2) invariant systems in d=8 and 7, respectively.