Plebanski action extended to a unification of gravity and Yang-Mills theory

We study a unification of gravity with Yang-Mills fields based on a simple extension of the Plebanski action to a Lie group $G$ which contains the local Lorentz group. The Coleman-Mandula theorem is avoided because the dynamics has no global spacetime symmetry. This may be applied to Lisi’s proposal of an $E8$ unified theory, giving a fully $E8$ invariant action. The extended form of the Plebanski action suggests a new class of spin foam models.

Figure 1

Disordered locality: A regular graph contaminated by nonlocal links.