Sean,
Maybe my insight into this is not complete hogwash. It will take a bit to digest the Gomes and Koslowski paper. BRST quantization is a cohomology of supergenerators, where this is a modern cornerstone of SUSY. It does appear this is derived from shape dynamics without reference to causal set theory. I'd be interested in contacting these two authors.
I agree that the isometry of the anti-de Sitter spacetime plays a role. The anti de Sitter spacetime exhibits periodic time which is removed by considering a universal cover or a patch on the spacetime. The AdS spacetime on this patch is
ds^2 = (1/x)(dt^2 + dx^2 - Σ_idz^idz^i)
which in the limit as x --> 0 defines a Minkowski metric
dx^2 = -dt^2 + Σ_idz^idz^i
which is a Minkowski spacetime. This means that the evolute of AdS from a spatial surface is an entire spacetime. So there is a loss of causality here. What is then required is a conformal completion of AdS. In doing so the Cauchy data on the AdS is defined on a conformal set of metrics. The boundary space ∂AdS_{n+1} is a Minkowski spacetime, or a spacetime E_n that is simply connected that with the AdS is such that (AdS_{n+1})UE_n is the conformal completion of AdS_{n+1} which exhibits a conformal completion under the discrete action of a Klienian group. For the Lorentzian group SO(2,n) there exists the discrete group SO(2,n,Z) which is a Mobius group. For a discrete subgroup Γ subset SO(2,n,Z) that obeys certain regular properties for accumulation points in the discrete set AdS_{n+1}/Γ is a conformal action of Γ on the sphere S_n. This is then a map which constructs an AdS ~ CFT correspondence.
The quotient space AdS/ Γ is a Kleinian structure. The group SO(2,n) is a map from the unit ball B_{n+1}, with boundary ∂B_{n+1} = S_n, into R^{n+1}. The discrete group Γ acts as a conformal on the sphere S^n by the action of the Mobius transformation on S_n. The discrete set of maps on S^n has accumulation points on the limit sphere S^n_∞ are determined by the limit set g_i \in G for i --> ∞. This is denoted by Λ(G), G = O(2,n). The discontinuous set is then the complement of this or Ω(G) = S_n - Λ(G). The manifold Ω(G)/G is an orbifold. This means that the Mobius transformation on the limit sphere S^2_∞ is equivalent to the conformal transformation of N^{n+1} which is equivalent to the isometries of AdS_{n+1}. The Ω(Γ)∩E_n/Γ is then a Lorentzian manifold ∂AdS_{n+1), and a set of discrete points in E_n pertaining to spatial hyperbolids of equivalent data. In this way the data on any spatial surface of AdS_{n+1} is contained in this conformal completeness of AdS_{n+1}. This is equivalent to the discrete action of Γ on S_n..
These discrete structures I think play a role analogous to causal set theory or to shape dynamics. I am of course not certain about this right now. I think this also has some connection to the AdS/CFT correspondence as well.
Cheers LC
