Spinor algebra transformations as gauge symmetry: limit to Einstein gravity

Abstract

We construct a Lagrangian of Weyl spinors and gauge fields, which is invariant under the action of equivalent local transformations on the spinor algebra representations. A model of vacuum with a nontrivial gauge strength-tensor setting a scale and spontaneously breaking the gauge symmetry is suggested, so that the leading approximation at low energies is described by the Einstein--Hilbert Lagrangian of gravity. We consider a mechanism for the cancellation of cosmological constant due to a symmetry between the vacuum strength tensor and the tensor dual to it. The appearance of nonzero masses for the non-graviton degrees of freedom for the gauge field is shown. The generalization to the Dirac spinors is considered, and a group of additional gauge symmetry is determined. We argue for a necessary introduction of supersymmetry.