2026/07/30 by Alberto S. Cattaneo, Filippo Fila-Robattino, Manuel Tecchiolli · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.DG #math.MP #math.SG
arxiv created 2026/08/01 · arxiv updated 2026/08/04
In this paper, the corner Poisson structure of four-dimensional Palatini-Cartan gravity is derived. Building on the classical description of gravity on manifolds with boundary, specifically on the boundary constraint algebra, a pre-Dirac structure on the space of corner fields is obtained together with a reduction procedure that yields a maximal Dirac structure, identified as the graph of a Poisson bivector field, on the reduced space of corner fields. It is further shown that this Poisson structure admits an equivalent affine Poisson description, which naturally exhibits the reduced corner theory as a BF-like theory and leads to a BF2V formulation. This provides the basis for a unified framework for the bulk, boundary, and corner structures of Palatini-Cartan gravity.