Analyze the corner symplectic contribution and edge modes

Analyze the corner contribution to the extended symplectic form for an arbitrary null hypersurface in the Weyl reference frame, in order to determine its role in the edge-mode content and in the interplay between the physical and reference manifolds.

Background

The embedding-field construction produces an extended phase space whose symplectic form contains both a bulk term and a corner term. The paper restricts its calculations to the bulk contribution, while the corner term is expected to encode information about edge modes and the relation between the physical spacetime and the dynamical reference manifold. Its explicit treatment is left unresolved.

References

However, as we will argue in the next subsections, for the purposes of this work we only deal with the bulk part of the symplectic potential, leaving the analysis of the corner potential to a future work.

— Higher spin dynamics in Weyl reference frame  (2608.16781 - Simone, 17 Aug 2026) in Section 2, subsection “Embedding field as DRF” and subsection “Poisson bracket”