Unification of Gravity and Yang-Mills Theory in (2+1)-Dimensions

Details Unification of Gravity and Yang-Mills Theory in (2+1)-Dimensions Unification of Gravity and Yang-Mills Theory in (2+1)-Dimensions

1992-11-10

arxiv.org/abs/gr-qc/9211014v1

Nucl.Phys. B395 (1993) 239-262

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22pages

Scientific paper

10.1016/0550-3213(93)90216-C

A gauge and diffeomorphism invariant theory in (2+1)-dimensions is presented in both first and second order Lagrangian form as well as in a Hamiltonian form. For gauge group $SO(1,2)$, the theory is shown to describe ordinary Einstein gravity with a cosmological constant. With gauge group $G^{tot}=SO(1,2)\otimes G^{YM}$, it is shown that the equations of motion for the $G^{YM}$ fields are the Yang-Mills equations. It is also shown that for weak $G^{YM}$ Yang-Mills fields, this theory agrees with the conventional Einstein-Yang-Mills theory to lowest order in Yang-Mills fields. Explicit static and rotation symmetric solutions to the Einstein-Maxwell theory are studied both for the conventional coupling and for this unified theory. In the electric solution to the unified theory, point charges are not allowed, the charges must have spatial extensions.

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