The Master-Space Teleparallel Supergravity: Accelerated frames

Using Palatini’s formalism extended in a plausible fashion to the recent MS gp-Supergravity (TerKazarian, 2023c, 2024b), subject to certain rules, we reinterpret a flat MS gp-SG theory with Weitzenb¨ock torsion as the quantum field theory of Master-Space Teleparallel Supergravity (MS gp-TSG), having the gauge translation group in tangent bundle. Here the spin connection represents only inertial effects, but not gravitation at all. In order to recover the covariance, we introduce a 1-form of the Yang–Mills connection assuming values in the Lie algebra of the translation group. The Hilbert action vanishes and the gravitino action loses its spin connections, so that the accelerated reference frame has Weitzenb¨ock torsion induced by gravitinos. Due to the soldered character of the tangent bundle, torsion presents also the anholonomy of the translational covariant derivative. The gauge invariance of the tetrad provides torsion invariance under gauge transformations. The role of the Cartan-Killing metric usually comes, when it exists, from its being invariant under the group action. Here it does not exist, but we use the invariant Lorentz metric of Minkowski spacetime in its stead. The action of MS gp-TSG is invariant under local translations, under local super symmetry transformations and by construction is invariant under local Lorentz rotations and under diffeomorphisms. So that this action is invariant under the Poincar´e supergroup and under diffeomorphisms. We show the equivalence of the Teleparallel Gravity action with Hilbert action, which proves that the immediate cause of the fictitious Riemann curvature for the LeviCivita connection arises entirely due to the inertial properties of the Lorentz-rotated frame of interest. The curvature of Weitzenb¨ock connection vanishes identically, but for a tetrad involving a non-trivial translational gauge potential, the torsion is non-vanishing. We consider Weitzenb¨ock connection a kind of dual of the Levi-Civita connection, which is a connection with vanishing torsion, and non-vanishing fictitious curvature. The Weitzenb¨ock connection defines the acceleration through force equation, with torsion (or contortion) playing the role of force.