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

@article{Smolin2009PlebanskiAE,
  title={Plebanski action extended to a unification of gravity and Yang-Mills theory},
  author={Lee Smolin},
  journal={Physical Review D},
  year={2009},
  volume={80},
  pages={124017}
}
  • L. Smolin
  • Published 6 December 2007
  • Mathematics
  • Physical Review D
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. 

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References

SHOWING 1-10 OF 26 REFERENCES

Towards a unification of gravity and Yang-Mills theory.

TLDR
The theory is shown to give the conventional Yang-Mills theory to the lowest order in the fields, and equals the Ashtekar formulation of gravity with a cosmological constant with gauge group $SO(3,C)$.

An Exceptionally Simple Theory of Everything

All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong

Gravi-weak unification

The coupling of chiral fermions to gravity makes use only of the selfdual SU(2) subalgebra of the (complexified) SO(3, 1) algebra. It is possible to identify the antiselfdual subalgebra with the

Gravity and Yang-Mills Theory:. Two Faces of the same Theory?

We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills phase space. The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first

Unified geometric theory of gravity and supergravity

A unified geometric formulation of gravitation and supergravity is presented. The action for these theories is constructed out of the components of the curvature tensor for bundle spaces with

NON-METRIC GRAVITY: A STATUS REPORT

We review the status of a certain (infinite) class of four-dimensional generally covariant gravity theories propagating two degrees of freedom that are formulated without any direct mention of the

Isogravity: Toward an Electroweak and Gravitational Unification

We present a model that unites the electroweak interaction with general relativity without specifying a space-time metric. This is made possible by embedding the kinetic terms for gravity and

Renormalizable Non-Metric Quantum Gravity?

We argue that four-dimensional quantum gravity may be essentially renormalizable if one relaxes the assumption of metricity of the theory. We work with Plebanski formulation of general relativity in

New variables for classical and quantum gravity.

  • Ashtekar
  • Physics
    Physical review letters
  • 1986
TLDR
A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced that enables one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory.