Abstract
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 an alternative construction.
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Cantcheff, M.B. General Relativity as a (Constrained) Yang-Mills Theory and a Novel Gravity with Torsion. General Relativity and Gravitation 34, 1781–1792 (2002). https://doi.org/10.1023/A:1020755822473
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DOI: https://doi.org/10.1023/A:1020755822473