# Weyl Covariant Quadratic Curvature Gravity in 3-Dimensional Riemann-Cartan-Weyl Space-Times

## TL;DR

This paper develops a Weyl covariant extension of quadratic curvature gravity in three dimensions within Riemann-Cartan-Weyl space-times, including the New Massive Gravity, ensuring a consistent scale-invariant framework.

## Contribution

It introduces a Weyl covariant formulation of quadratic curvature gravity in 3D Riemann-Cartan-Weyl space-times, extending existing theories like New Massive Gravity.

## Key findings

- Weyl gauging yields a consistent generalisation for certain quadratic curvature theories.
- The approach maintains local scale invariance in 3D gravity models.
- The formulation includes and extends the New Massive Gravity theory.

## Abstract

We discuss locally Weyl (scale) covariant generalisation of quadratic curvature gravity theory in three dimensions using Riemann-Cartan-Weyl space-times. We show that this procedure of Weyl gauging yields a consistent generalisation for a particular class of quadratic curvature gravity theories which includes the New Massive Gravity theory.