### 2.2 Smolin’s lattice model

The first gauge-theoretic model for lattice gravity is due to Smolin [186], based on the continuum
formulation of MacDowell and Mansouri [157], with de Sitter gauge group or , and a
Lagrangian of -type,
where the components of are related to those of the usual curvature tensor by
Although the underlying gauge potentials are - or -valued, the action is only
invariant under the 6-dimensional subgroup of Lorentz transformations. The theory contains a dimensionful
parameter . The gauge potentials associated with the internal 5-direction are identified with the frame
fields , and the action can be decomposed into the usual Einstein-term (1) plus a cosmological constant
term with and a topological -term. Smolin analyzed its lattice discretization, and found
both a weak- and a strong-coupling phase, with respect to the dimensionless coupling constant
. He performed a weak-coupling expansion about flat space and rederived the usual
propagator. In the strong-coupling regime he found massive excitations and a confining property for
spinors.