General relativity and the AKSZ construction (Q2041640)

In the article under reviewing the authors apply the previous Alexandrov-Kontsevich-Schwarz-Zaboronski ( AKSZ) construction [\textit{M. Alexandrov} et al., Int. J. Mod. Phys. A 12, No. 7, 1405--1429 (1997; Zbl 1073.81655)] to the Batalin-Fradkin-Vilkovysky description of the reduced phase space both Einstein-Hilbert action and of the Palatini-Cartan theory in every space-time dimension greater than 2. The authors make a comparison between the case of Einstein-Hilbert and Palatini-Cartan cases. One found that in the previous ( PC) case one recover a Batalin-Vilkovysky theory for the first order formulation of an Einstein-Hilbert theory. While in the later case one agree with Batalin-Vilkovysky theory for Palatini-Cartan theory with partial implementation of the torsion-free condition. All the theories investigated here are Batalin-Vilkovysky versions of the same classical system on cilinders. The study given here have the advantage of giving a compatible BV-Batalin-Fradkin-Vilkovysky description which represents a necessary starting point for quantization in a presence of a boundary.