Quantum Gravity Model in the framework of Weyl-Cartan geometry

TL;DR

This paper explores a quantum gravity model within Weyl-Cartan geometry, highlighting how Weyl vector fields influence the metric's dynamics through quantum corrections and their relation to torsion fields, resulting in a Maxwell-like Lagrangian.

Contribution

It introduces a quantum gravity framework in Weyl-Cartan geometry where Weyl vector fields induce dynamical metric behavior and relate to torsion, leading to a Maxwell-like Lagrangian.

Findings

Weyl vector fields can induce dynamical symmetry breaking in quantum gravity.

A relation between Weyl vector fields and torsion fields is established in low energy regimes.

The resulting Lagrangian resembles Maxwell electrodynamics.

Abstract

We study the Weyl vector fields which can play an important role in quantum gravity. The metric obtains its dynamical content after dynamical symmetry breaking in the phase of the effective Einstein gravity which is induced by quantum Weyl corrections. In low energy regime with scalar field there is a relation between the Weyl vector fields and the torsion fields. If this condition is given to Weyl vector fields and torsions, then the Lagrangian becomes like Maxwell type.