A minimal model of Lorentz gauge gravity with dynamical torsion

TL;DR

This paper introduces a minimal Lorentz gauge gravity model with R^2-type Lagrangian, analyzing its degrees of freedom, quantization, and potential emergence of Einstein gravity from torsion dynamics.

Contribution

It proposes a new gravity model with dynamical torsion, demonstrating its degrees of freedom and quantization, and explores how Einstein gravity may emerge from torsion quantum effects.

Findings

Model admits a topological phase with arbitrary metric.

Number of torsion degrees of freedom equals metric's physical degrees.

Spin two torsion mode becomes dynamical due to non-linearity.

Abstract

A new Lorentz gauge gravity model with R^2-type Lagrangian is proposed. In the absence of classical torsion the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space-time background using the Lagrange formalism and demonstrate that the model possesses a minimal set of dynamic degrees of freedom for the torsion. Surprisingly, the number of torsion dynamic degrees of freedom equals the number of physical degrees of freedom for the metric tensor. An interesting feature of the model is that the spin two mode of torsion becomes dynamical essentially due to the non-linear structure of the theory. We perform covariant one-loop quantization of the model for a special case of constant curvature space-time background. We treat the contortion as a quantum field variable whereas the metric tensor is kept as a classical object. We discuss a possible mechanism of an emergent Einstein gravity as a part of the effective theory induced due to quantum dynamics of torsion.