Gravity and Induced Effective Theories

We develop the gauge approach based on the Lorentz group to the gravity with torsion. With a Lagrangian quadratic in curvature we show that the Einstein-Hilbert action can be induced from a simple gauge model due to quantum corrections of torsion via formation of a gravito-magnetic condensate. An effective theory of cosmic knots at Planckian scale is proposed. 1. Utiyama-Kibble-Sciama gauge approach to gravity The gauge approach to gravity based on Lorentz and Poincare group was proposed in [1] and later was developed in many studies (see refs. in [2]). The Lorentz gauge models were further studied by Carmeli [3]. The possibility of inducing the Einstein gravity via quantum corrections was considered by many physicists in various models [4]. In most of these models the Einstein-Hilbert term is induced by quantum corrections due to interaction with matter fields. In the present article we propose a simple gauge model of quantum gravity based on the Lorentz group as a structural group. In the framework of this gauge model we demonstrate that even in a pure quantum gravity case with torsion the Einstein-Hilbert action can be induced due to the quantum dynamics of torsion via formation a nontrivial vacuum with a gravito-magnetic condensate. We develop the gauge approach to the gravity by suggesting that the torsion represents exactly the dynamical variable of quantum gravity. Moreover, we conjecture that the torsion can be confined and exists intrinsically as a quantum object, and its quantum dynamics manifests itself by inducing the Einstein-Hilbert theory as an effective theory of quantum gravity. We start with the formalism of the Lorentz gauge model along the lines proposed in [1]. The vielbein ea is treated as a fixed background field which obtains the dynamical content after inducing the Hilbert-Einstein term in the effective theory. The covariant derivative with respect to the Lorentz structural group is defined in a standard manner Da = e μ a(∂μ +Aμ), (1) where Aμ ≡ AμcdΩ is a general affine connection taking values in Lorentz Lie algebra. The original Lorentz gauge transformation is the following δeμa = Λ b ae μ b , δAμ = −∂μΛ− [Aμ,Λ], (2)