Projective transformations in metric-affine and Weylian geometries

TL;DR

This paper explores how projective transformations can be generalized in certain geometries relevant to gravity theories, revealing new ways to interpret gauge potentials and invariances.

Contribution

It introduces generalized projective transformations in metric-affine and Weylian geometries and shows their role in recasting gravity models with different gauge invariances.

Findings

Recasting Riemann-Cartan-Weyl geometry via projective invariance

Identifying torsion vector as Weyl gauge potential

Establishing links between projective transformations and gravity models

Abstract

We discuss generalizations of the notions of projective transformations acting on affine model of Riemann-Cartan and Riemann-Cartan-Weyl gravity which preserve the projective structure of the light-cones. We show how the invariance under some projective transformations can be used to recast a Riemann-Cartan-Weyl geometry either as a model in which the role of the Weyl gauge potential is played by the torsion vector, which we call torsion-gauging, or as a model with traditional Weyl (conformal) invariance.