Matrix Gravity and Massive Colored Gravitons

TL;DR

This paper develops a matrix-valued gravity theory with a complex vierbein and gauge symmetry, resulting in a spectrum of one massless and multiple massive gravitons through spontaneous symmetry breaking.

Contribution

It introduces a novel matrix-valued vierbein framework with SL(2N,C) gauge symmetry, enabling spontaneous symmetry breaking and mass generation for gravitons.

Findings

Spectrum includes one massless and multiple massive gravitons.

Fields for non-compact generators acquire correct kinetic energies.

Yang-Mills fields gain proper kinetic terms via coupling to vierbein components.

Abstract

We formulate a theory of gravity with a matrix-valued complex vierbein based on the SL(2N,C)xSL(2N,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,C) then the spectrum would correspond to one massless graviton coupled to $2N^2 -1$ massive gravitons. A novel feature is the way the fields corresponding to non-compact 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 non-dynamical antisymmetric components of the vierbeins.