# Dynamics of 3-Forms in Seven Dimensions

## TL;DR

This paper investigates a dynamical theory of 3-forms in seven dimensions, revealing its degrees of freedom and connections to 4D scalar-tensor gravity through dimensional reduction.

## Contribution

It introduces a non-linear 7D 3-form theory, analyzes its degrees of freedom, and explores its reduction to a 4D scalar-tensor gravity variant.

## Key findings

- The 7D theory propagates 3 degrees of freedom.
- Dimensional reduction yields a 4D scalar-tensor gravity variant.
- The theory extends the analogy of Chern-Simons to higher dimensions.

## Abstract

We continue to study a certain dynamical theory of 3-forms in seven dimensions, which can be viewed as a non-linear 7D analog of the 3D Abelian Chern-Simons theory. We perform the 6+1 split and show that the theory propagates 3 degrees of freedom. We also study the dimensional reduction on S3. We find the resulting theory to be a variant of 4D scalar-tensor theory of gravity.