Yang-Mills sources in biconformal gravity
Abstract
Biconformal gravity, based on gauging of the conformal group to 2n dimensions, reproduces n-dim scale-covariant general relativity on the co-tangent bundle in any dimension. We generalize this result to include Yang-Mills matter sources formulated as SU\left(N\right) gauge theories with a twisted action on the full 2n-dimensional biconformal space. We show that the coupling of the sources to gravity does not stop the reduction of effective dimension 2n\rightarrow n of the gravity theory, and instead forces the Yang-Mills source to reduce to ordinary n-dimensional Yang-Mills theory on the gravitating cotangent bundle, with the usual Yang-Mills energy tensor as gravitational source. The results apply as well to gravity with sources on K\"ahler manifolds and in double field theories.
Cite
@article{arxiv.2010.13001,
title = {Yang-Mills sources in biconformal gravity},
author = {Davis W. Muhwezi and James T. Wheeler},
journal= {arXiv preprint arXiv:2010.13001},
year = {2021}
}
Comments
67 pages including appendices and references Clarified discussion of Kahler and Killing forms; added discussion of alternative Weyl gravity sources