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 O(5)-formulation which reduces to the Poincaré form in the limit as the length of some preferred O (5)-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.

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