Weyl covariant theories of gravity in 3-dimensional Riemann-Cartan-Weyl space-times

Abstract

We discuss locally Weyl (scale) covariant generalisations of gravitational theories using Riemann-Cartan-Weyl space-times in arbitrary dimensions. We illustrate the procedure of Weyl gauging for three examples: general relativity, topologically massive gravity and minimal massive gravity theories in three dimensions. Afterwards, we demonstrate the consistency of scale covariant generalisation by showing that the scale covariant theories contain the original theories in their vacuum configuration for their Weyl sector.