Gravity and Mirror Gravity in Plebanski Formulation

Abstract

We present several theories of four-dimensional gravity in the Plebanski formulation, in which the tetrads and the connections are the independent dynamical variables. We consider the relation between different versions of gravitational theories: Einstenian, dual, 'mirror' gravities and gravity with torsion. According to Plebanski's assumption, our world, in which we live, is described by the self-dual left-handed gravity. We propose that if the Mirror World exists in Nature, then the 'mirror gravity' is the right-handed anti-self-dual gravity with broken mirror parity. Considering a special version of the Riemann-Cartan space-time, which has torsion as additional geometric property, we have shown that in the Plebanski formulation the ordinary and dual sectors of gravity, as well as the gravity with torsion, are equivalent. In this context, we have also developed a 'pure connection gravity' -a diffeomorphism-invariant gauge theory of gravity. We have calculated the partition function and the effective Lagrangian of this four-dimensional gravity and have investigated the limit of this theory at small distances.

Standard model and graviweak unification with (super)renormalizable gravity. Part I: Visible and invisible sectors of the universe

“…Originally General Relativity (GR) was formulated by Einstein as the dynamics of a metric, g µν . Later Plebanski [31], Ashtekar [32,33] and other authors [34,35] presented GR in a self-dual approach, in which the true configuration variable is a self-dual connection corresponding to the gauging of the local Lorentz group, SO(1, 3), or the spin group, Spin (1,3). In the unification models [1,2], the fundamental variable is a connection, A, valued in a Lie algebra, g, that includes a subalgebrag:…”

“…Following the ideas of Ref. [3], we distinguish the two worlds of the Universe, visible and invisible, and consider the two sectors of gravity: left-handed gravity and right-handed gravity. The self-dual left-handed gravity is described by the following action:…”

“…Developing the ideas of Refs. [1,3], we distinguish the Left and Right worlds of the Universe, considering the graviweak unified model in both sectors of the Universe, visible and invisible, which are described respectively by the following connections:…”

“…In the paper [1], using a general model [2] of the unification of gravity with SU(N) or SO(N) gauge and Higgs fields, we presented a model of unification of gravity with weak SU(2) gauge and Higgs fields, developing the ideas of Ref. [3]. We have considered a Spin(4, 4)-group of the graviweak unification, which is spontaneously broken into the SL(2, C) (grav) × SU(2) (weak) .…”

Gravi-weak unification and the black-hole-hedgehog’s solution with magnetic field contribution

“…[7][8][9][10], using results of Refs. [11,12], we have constructed the Gravi-Weak unification (GWU), considering a Spin(4, 4)-group of GWU spontaneously broken into the SL(2, C) (grav) × SU(2) (weak) group of symmetry. In agreement with experimental and astrophysical results, we assumed that after the Big Bang, there came into being the unification group G T OE of the Theory of the Everything (TOE) which was rapidly broken down to the direct product of series of gauge groups (see Ref.…”