Plebanski Action

When we again do the compactification trick we find the Plebanski action
S = ∫_T⁴d⁴xϵ^abcd[B_cdKF^K_ab + Φ_IJB^I_abB^J_cd]
You can read this new derivation of the Plebanski action in the recent article by Lee Smolin Matrix universality of gauge and gravitational dynamics.

Smolin ends his article with the following:

"Conjecture: There is a universality class of cutoff background independent theories of connections, which are all equivalent to each other in the sense that there are transformations that map the degrees of freedom of any one into the degrees of freedom of the other, preserving the equations of motion. Representatives of this equivalence class include general relativity in d = 4 coupled to Yang-Mills theory for any U (N ) (plus certain degrees of freedom required to complete the unification) as well as Chern-Simons theory, matrix Chern-simons theory, as well as the matrix model (2)."

Where (2) is:

S = TrM³

His final conclusion is:

"If true, this hypothesis imply that the question of why particular laws and degrees of freedom are observed in our universe is just part of the question of what chooses the initial conditions in cosmology. A universality of dynamics such as conjectured here would mean that the question of what is the ”ultimate theory” may play as minor a role in physics as the choice of physical computer plays in computer science."

The ideas in this article have been discussed with Roberto Mangabeira Unger, one of the leading thinkers of our time.