A Minimal Model of Lorentz Gauge Gravity With Dynamical Torsion

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.

Lorentz gauge theory as a model of emergent gravity

“…It has been shown that the model described by the Lagrangian (13) admits dynamical degrees of freedom for the contortion only for the special values of the parameters, ¼ 0, ¼ À3 with overall normalization factor [13]. The result has been obtained from the analysis of linearized equations of motion for contortion in the presence of constant Riemann curvature space-time background.…”

“…If the contortion still possesses dynamical properties in flat space-time, then another important question arises, at which values of the parameters , , it will happen. In the present paper, we will mainly concentrate on flat metric limit, i.e., a pure Lorentz gauge theory with the Lagrangian of type (13). The field strength (curvature tensor) in flat space-time takes a simple form…”

“…The most general Lagrangian quadratic in Riemann-Cartan curvature and with the Einstein-Hilbert term was considered in [12]. Recently, a Lorentz gauge gravity model with the contortion part in the Lorentz gauge connection that admits a topological phase for gravitation has been proposed [13]. We assume that such a topological phase can be possibly realized at very early stages of our Universe close to or before the big bang.…”

“…By this way, we keep the gauge structure of the considered Lorentz gauge gravity models close to standard gauge approach. It has been shown [13] that there is a model with a special R 2 -type Lagrangian that admits a topological phase for the gravitation whereas contortion still possesses dynamical degrees of freedom. An interesting feature of the model is that the number of dynamical degrees of freedom of torsion is the same as the number of physical degrees of the metric tensor.…”

“…This gives a hint that torsion may play a role of quantum counterpart to the classical metric of Einstein gravity, which is supposed to be an effective theory generated by the quantum dynamics of torsion [34]. The analysis of dynamic content of the model in [13] has been performed at the lowest linearized level in the contortion part and in the presence of constant Riemann curvature space-time background. Because of these limitations, several important issues in this model remain unclear, especially whether the dynamical properties of torsion are intrinsic properties or they depend on the presence of the background metric.…”