Generalized Yang-Mills Theory and Gravity

TL;DR

This paper introduces a generalized Yang-Mills framework that encompasses gravity theories, including Einstein gravity, by relaxing algebraic factorization constraints, and suggests a more transparent connection between Yang-Mills and gravity scattering amplitudes.

Contribution

It extends Yang-Mills theory to include gravity-like interactions through non-factorized algebras, unifying different theories under a common generalized framework.

Findings

Gravity theories can be formulated as generalized Yang-Mills theories.

The approach clarifies the connection between Yang-Mills and gravity amplitudes.

Includes Einstein gravity as a special case within the generalized framework.

Abstract

We propose a generalization of Yang-Mills theory for which the symmetry algebra does not have to be factorized as mutually commuting algebras of a finite-dimensional Lie algebra and the algebra of functions on base space. The algebra of diffeomorphism can be constructed as an example, and a class of gravity theories can be interpreted as generalized Yang-Mills theories. These theories in general include a graviton, a dilaton and a rank-2 antisymmetric field, although Einstein gravity is also included as a special case. We present calculations suggesting that the connection in scattering amplitudes between Yang-Mills theory and gravity via BCJ duality can be made more manifest in this formulation.