# Supersymmetric Yang-Mills Theory as Higher Chern-Simons Theory

## TL;DR

This paper explores how string field theory actions for topological sigma models relate to higher Chern-Simons theories, proposing a new supersymmetric Yang-Mills theory formulation on ambitwistor space.

## Contribution

It introduces a novel higher ambitwistor space action functional for maximally supersymmetric Yang-Mills theory based on higher Chern-Simons theory.

## Key findings

- Higher Chern-Simons theories describe connective structures on higher bundles
- Proposed a supersymmetric Yang-Mills action on higher ambitwistor space
- Established connections between string field theory and categorified gauge theories

## Abstract

We observe that the string field theory actions for the topological sigma models describe higher or categorified Chern-Simons theories. These theories yield dynamical equations for connective structures on higher principal bundles. As a special case, we consider holomorphic higher Chern-Simons theory on the ambitwistor space of four-dimensional space-time. In particular, we propose a higher ambitwistor space action functional for maximally supersymmetric Yang-Mills theory.