Matrix gravity and massive colored gravitons

Abstract

We formulate a theory of gravity with a matrix-valued complex vierbein based on the $SL(2N,\mathbb{C})\ensuremath{\bigotimes}SL(2N,\mathbb{C})$ gauge symmetry. The theory is metric independent, and before symmetry breaking all fields are massless. The symmetry is broken spontaneously and all gravitons corresponding to the broken generators acquire masses. If the symmetry is broken to $SL(2,\mathbb{C})$, then the spectrum would correspond to one massless graviton coupled to $2{N}^{2}\ensuremath{-}1$ massive gravitons. A novel feature is the way the fields corresponding to noncompact generators acquire kinetic energies with correct signs. Equally surprising is the way Yang-Mills gauge fields acquire their correct kinetic energies through the coupling to the nondynamical antisymmetric components of the vierbeins.