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