Gravity = Yang-Mills

TL;DR

This paper explores a broad class of Yang-Mills-type theories using homotopy algebras, demonstrating that gravity can be formulated as a tensor product of kinematic algebras, unifying gauge theories and gravity.

Contribution

It introduces a generalized framework for Yang-Mills theories using homotopy algebras, showing gravity as a tensor product of kinematic structures, extending the conventional understanding.

Findings

Standard Yang-Mills is a special case within a broader class.

Gravity can be represented as a tensor product of kinematic algebras.

Anomalies can be canceled with a second copy of the kinematic algebra.

Abstract

This essay's title is justified by discussing a class of Yang-Mills-type theories of which standard Yang-Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of homotopy algebras, where conventional Yang-Mills theory is the tensor product ${\cal K}\otimes \frak{g}$ of a `kinematic' algebra ${\cal K}$ with a color Lie algebra $\frak{g}$. The larger class of Yang-Mills-type theories are given by the tensor product of ${\cal K}$ with more general Lie-type algebras of which ${\cal K}$ itself is an example, up to anomalies that can be cancelled for the tensor product with a second copy $\bar{\cal K}$. Gravity is then given by ${\cal K}\otimes \bar{\cal K}$.