Going down from a 3-form in 16 dimensions

TL;DR

This paper explores a special self-duality equation for 3-forms in 16 dimensions based on group theory, leading to new insights in topological field theories, supersymmetry, and gravitational models in lower dimensions.

Contribution

It introduces a novel self-duality equation for 3-forms in 16D and discusses its implications for topological theories, supersymmetry, and octonionic gravity.

Findings

Existence of an $SO(8) imes SO(7)$ invariant self-duality equation in 16D.

Dimensional reduction yields new supersymmetric theories in 4D and lower.

Development of an octonionic gravitational self-duality model in 8D.

Abstract

Group theory indicates the existence of a $SO(8) X SO(7) \subset SO(16)$ invariant self-duality equation for a 3-form in 16 dimensions. It is a signal for interesting topological field theories, especially on 8-dimensional manifolds with holonomy group smaller than or equal to Spin(7), with a gauge symmetry that is SO(8) or SO(7). Dimensional reduction also provides new supersymmetric theories in 4 and lower dimensions, as well as a model with gravitational interactions in 8 dimensions, which relies on the octonionic gravitational self-duality equation.