General Relativity as a (constrained) Yang-Mills's Theory and a Novel Gravity with Torsion
Abstract
Description
We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D-1,2) (or SO(D,1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR appear as solutions of a genuine SO(D-1,1)-YM.
We also present a theory of gravity with torsion as the most natural extension of this result. The theory comes out to be strictly an YM-theory upon relaxation of a suitable constraint. This work sets out to enforce the close connection between YM theories and GR by means of a new construction.
8 pages. This replaced version has slightly modified title, some additional information that render our results clearer and a few new contributions. References added
8 pages. This replaced version has slightly modified title, some additional information that render our results clearer and a few new contributions. References added