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

Understand

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 theory 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.