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

TL;DR

This paper extends the Plebanski action to unify gravity with Yang-Mills fields using a Lie group extension, avoiding the Coleman-Mandula theorem, and proposes new spin foam models with potential applications to E8 unification.

Contribution

It introduces a novel extension of the Plebanski action to include a Lie group G, enabling gravity-Yang-Mills unification without global spacetime symmetries.

Findings

Proposes a fully E8 invariant action for unification.

Suggests a new class of spin foam models.

Avoids the Coleman-Mandula no-go theorem.

Abstract

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.