Non-Topological Gauss-Bonnet type model of gravity with torsion

TL;DR

This paper introduces a non-topological Gauss-Bonnet type gravity model with torsion that admits propagating torsion fields, features reduced dynamical degrees of freedom, and explores its quantum properties and potential emergence of Einstein gravity.

Contribution

It presents a novel non-topological Gauss-Bonnet type gravity model with propagating torsion and analyzes its quantum behavior and implications for emergent gravity.

Findings

The model admits propagating torsion unlike topological Lovelock gravity.

The torsion degrees of freedom are reduced to spin two, U(1) gauge vector, and spin zero fields.

The Hamiltonian's kinetic part for the spin two field is positively defined.

Abstract

A non-topological Lorentz gauge model of gravity with torsion based on Gauss-Bonnet type Lagrangian is considered. The Lagrangian differs from the Lovelock term in four-dimensional space-time and has a number of interesting features. We demonstrate that the model admits a propagating torsion unlike the case of the topological Lovelock gravity. Due to additional symmetries of the proposed Gauss-Bonnet type Lagrangian the torsion has a reduced set of dynamical degrees of freedom corresponding to the spin two field, U(1) gauge vector field and spin zero field. A remarkable feature is that the kinetic part of the Hamiltonian containing the spin two field is positively defined. We perform one-loop quantization of the model for a special case of constant Riemann curvature space-time background treating the torsion as a quantum field variable. We discuss a possible mechanism of emergent Einstein gravity as an effective theory which can be induced due to quantum dynamics of torsion.