Gravity = Yang-Mills

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 $\mathcal{K}\otimes \mathfrak{g}$ of a `kinematic’ algebra $\mathcal{K}$ with a color Lie algebra $\mathfrak{g}$. The larger class of Yang-Mills-type theories are given by the tensor product of $\mathcal{K}$ with more general Lie-type algebras of which $\mathcal{K}$ itself is an example, up to anomalies that can be cancelled for the tensor product with a second copy $\bar{\mathcal{K}}$. Gravity is then given by $\mathcal{K}\otimes \bar{\mathcal{K}}$.