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A number of approaches to gravitation have much in common with the gaugetheories of the standard model of particle physics. In this paper, we developthe Hamiltonian formulation of a class of gravitational theories that may beregarded as spontaneously-broken gauge theories of the complexified Lorentzgroup $SO(1,3)_C$ with the gravitational field described entirely by a gaugefield valued in the Lie algebra of $SO(1,3)_C$ and a `Higgs field' valued inthe group's fundamental representation. The theories have one free parameter$\beta$ which appears in a similar role to the inverse of the Barbero-Immirziparameter of Einstein-Cartan theory. However, contrary to that parameter, it isshown that the number of degrees of freedom crucially depends on the value of$\beta$. For non-zero values of $\beta$, it is shown that three complex degreesof freedom propagate on general backgrounds, and for the specific values$\beta=\pm i$ an extension to General Relativity is recovered in asymmetry-broken regime. For the value $\beta=0$, the theory propagates no localdegrees of freedom. A non-zero value of $\beta$ corresponds to the self-dualand anti-self-dual gauge fields appearing asymmetrically in the action,therefore in these models, the existence of gravitational degrees of freedom istied to chiral asymmetry in the gravitational sector.

Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group