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 K circle times g of a 'kinematic' algebra K with a color Lie algebra g. The larger class of Yang-Mills-type theories are given by the tensor product of K with more general Lie-type algebras, of which K itself is an example, up to anomalies that can be canceled for the tensor product with a second copy K over bar . Gravity is then given by K circle times K over bar .

Automated summary

This essay justifies its title by discussing a class of Yang-Mills-type theories that include standard Yang-Mills theories and gravity as a double field theory. The framework of homotopy algebras is used, where conventional Yang-Mills theory is represented as the tensor product K circle times g of a 'kinematic' algebra K with a color Lie algebra g. The broader class of Yang-Mills-type theories are given by the tensor product of K with more general Lie-type algebras, including K itself, up to cancelable anomalies when combined with a second copy K over bar. Gravity is then represented by K circle times K over bar.