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

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.