Master Space-Teleparallel Supergravity: Implications for Special Cases

Abstract

We propose the theory of Master space-Teleparallel Supergravity (\(\widetilde{\textrm{MS}}_{p}\)-TSG), subject to certain rules, as a local extension of the author’s recent theory of global MS\({}_{p}\)-SUSY [1]. The latter reviews the physical processes underlying the standard Lorenz code of motion and its deformation tested in experiments for ultra-high energy cosmic ray and TeV-\(\gamma\) photons observed. A local MS\({}_{p}\)-SUSY theory was originally conceived as a theory of \(\widetilde{\textrm{MS}}_{p}\)-supergravity (SG). The action of the simple \(\widetilde{\textrm{MS}}_{p}\)-SG theory includes the Hilbert term for a fictitious graviton coexisting with a fictitious gravitino (sparticle) described by the Rarita–Scwinger kinetic term. Using Palatini’s formalism extended in a plausible fashion to this theory, we reinterpret the flat \(\widetilde{\textrm{MS}}_{p}\)-SG theory with Weitzenböck torsion as the theory of \(\widetilde{\textrm{MS}}_{p}\)-TSG having the gauge translation group in the tangent bundle. The Hilbert action here vanishes, and the gravitino action loses its spin connections, so that the accelerated reference frame has a Weitzenböck torsion induced by gravitinos. The action of \(\widetilde{\textrm{MS}}_{p}\)-TSG is invariant under the Poincaré supergroup and under diffeomorphisms. The Weitzenböck connection defines the acceleration through force equation, with torsion (or contortion) playing the role of force. The accelerated particle mechanics in 4D Minkowski space–time is discussed. We develop a general deformation of the flat master space (MS\({}_{p}\to\widetilde{\textrm{MS}}_{p}\)), and show that the occurrence of inertial effects is clearly caused by that. We supplement the \(\widetilde{\textrm{MS}}_{p}\)-TSG theory by considering the consequences for the Newtonian limit, the uniform acceleration field and the relativistic inertial force in Minkowski and semi-Riemannian spaces. The Weak Equivalence Principle (WEP) is a consequence of the theory.