G_2 invariant 7D Euclidean super Yang-Mills theory as a higher-dimensional analogue of the 3D super-BF theory

TL;DR

This paper constructs a higher-dimensional super Yang-Mills theory with G_2 invariance, linking it to lower-dimensional super-BF theories, and clarifies its formulation without extra constraints.

Contribution

It presents a new formulation of 8D super Yang-Mills with generalized self-duality, reducing to a G_2-invariant 7D super Yang-Mills, as an analogue of 3D super-BF theory.

Findings

Formulation of 8D super Yang-Mills avoiding extra constraints

Reduction to 7D G_2-invariant super Yang-Mills

Further reduction yields 3D super-BF theory with hypermultiplet

Abstract

A formulation of the N_T=1, D=8 Euclidean super Yang-Mills theory with generalized self-duality and reduced Spin(7)-invariance is given which avoids the peculiar extra constraints of Nishino and Rajpoot, hep-th/0210132. Its reduction to 7 dimensions leads to the G_2-invariant N_T=2, D=7 super Yang-Mills theory which may be regarded as a higher-dimensional analogue of the N=2, D=3 super-BF theory. When reducing further that G_2-invariant theory to 3 dimensions one gets the N_T=2 super-BF theory coupled to a spinorial hypermultiplet.