Yang-Mills gravity in biconformal space

TL;DR

This paper develops a gravity theory based on Yang-Mills actions within biconformal space, linking conformal symmetry, scale invariance, and flat space gauge theories, offering new insights into gravitational and gauge interactions.

Contribution

It introduces a novel biconformal gauging approach to formulate Yang-Mills gravity and systematically extends 4D Yang-Mills theories to biconformal space, establishing a direct correspondence between gravity and gauge theories.

Findings

Describes 4D, scale-invariant general relativity for slowly changing fields.

Provides a systematic method to extend 4D Yang-Mills theories to biconformal space.

Establishes a one-to-one mapping between gravitational gauge theories and flat space gauge theories.

Abstract

We write a gravity theory with Yang-Mills type action using the biconformal gauging of the conformal group. We show that the resulting biconformal Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity in the case of slowly changing fields. In addition, we systematically extend arbitrary 4-dim Yang-Mills theories to biconformal space, providing a new arena for studying flat space Yang-Mills theories. By applying the biconformal extension to a 4-dim pure Yang-Mills theory with conformal symmetry, we establish a 1-1, onto mapping between a set of gravitational gauge theories and 4-dim, flat space gauge theories.