GRAVITY WITHOUT METRIC, TORSION, AND TOPOLOGICAL GRAVITY

The role of θ term in gravity without the metric formulation of Capovilla, Jacobson, and Dell has been investigated when the gauge group is taken to be SL(2,C) and it is shown that this corresponds to the introduction of torsion and as such represents the Einstein-Cartan action. Moreover, as this term is related to the chiral anomaly, this helps us to formulate the Einstein-Hilbert gravitational action as a symmetry-breaking effect in quantum field theory. In view of this one can consider this topological θ term as the fundamental entity. When the chiral nature of matter field is not manifested explicitly, the torsion term effectively gives rise to the cosmo-logical constant. In case there is only the θ term in the action, one can have topological gravity which helps to realize physically Donaldson's theory of four-dimensional space-time geometry. © 1995 American Institute of Physics.