Yang-Mills sources in biconformal gravity

TL;DR

This paper extends biconformal gravity to include Yang-Mills sources, showing that these sources reduce to standard n-dimensional Yang-Mills theory on the cotangent bundle, preserving the effective dimension of the gravity theory.

Contribution

It generalizes biconformal gravity to incorporate SU(N) Yang-Mills sources, demonstrating their reduction to standard Yang-Mills theory without altering the effective dimension.

Findings

Yang-Mills sources reduce to n-dimensional Yang-Mills theory on the cotangent bundle.

Coupling to sources does not prevent the dimension reduction in biconformal gravity.

Results are applicable to gravity on Kähler manifolds and double field theories.

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.