Supertranslations in Higher Dimensions Revisited

TL;DR

This work addresses whether soft graviton theorems in higher even dimensions can be understood as Ward identities of an asymptotic symmetry, specifically supertranslations. By relaxing certain $u$-fall-off boundary conditions at null infinity and employing the covariant phase space formalism in linearized gravity, the authors derive finite, nontrivial supertranslation charges in arbitrary even dimensions and show their Ward identities reproduce the leading soft graviton theorem. A detailed six-dimensional analysis demonstrates the separation of divergent and finite contributions to the symplectic potential, yielding a concrete soft charge that, combined with hard (matter) contributions, matches the expected soft theorem; this motivates a generalized CK constraint framework that scales with dimension. The paper then extends these constructions to general even dimensions, providing a universal soft charge formula and clarifying the necessary CK-like constraints to count independent leading soft gravitons, while also discussing non-linear regime challenges and future extensions including massive fields and potential connections to subleading soft theorems.

Abstract

In this paper, we revisit the question of identifying Soft Graviton theorem in higher (even) dimensions with Ward identities associated with Asymptotic symmetries. Building on the prior work of \cite{strominger}, we compute, from first principles, the (asymptotic) charge associated to Supertranslation symmetry in higher even dimensions and show that (i) these charges are non-trivial, finite and (ii) the corresponding Ward identities are indeed the soft graviton theorems.