### 2.7 Assorted topics

Caselle et al. [70] proposed a lattice action that is genuinely Poincaré-invariant, at the price of
introducing additional lattice “coordinate variables”. They also suggested a compact -formulation
which reduces to the Poincaré form in the limit as the length of some preferred -vector is taken to
infinity, as well as a super-version involving the graded Poincaré group. The same authors
in [69] put forward an argument for why doubling should appear in general gravity plus matter
systems.
Reisenberger [175] has recently suggested a gauge-theoretic path integral based on the Plebanski action
for Euclidean gravity. He discretizes the theory on a simplicial or hypercubic lattice with group- and
algebra-valued fields. A metricity constraint needs to be imposed on the basic spin-1 fields, which it turns
out is difficult to treat exactly.