Understand
We investigate whether a spontaneously-broken gauge theory of the group $SU(2,2)$ may be a genuine competitor to General Relativity.
- The basic ingredients of the theory are an $SU(2,2)$ gauge field $A_{\mu}$ and a Higgs field $W$ in the adjoint representation of the group with the Higgs field producing the symmetry breaking $SU(2,2)\rightarrow SO(1,3)\times SO(1,1)$.
- The action for gravity is polynomial in $\{A_{\mu},W\}$ and the field equations are first-order in derivatives of these fields.
- The new $SO(1,1)$ symmetry in the gravitational sector is interpreted in terms of an emergent scale symmetry and the recovery of conformalized General Relativity and fourth-order Weyl conformal gravity as limits of the theory- following imposition of Lagrangian constraints- is demonstrated.