The asymptotic charges of Curtright dual graviton and Curtright extensions of BMS algebra

Abstract

This paper studies the asymptotic gauge charges of the Curtright mixed-symmetry rank-3 field $\phi_{[\rho\sigma]\nu}$ in Minkowski spacetime, interpreted in $ D = 5 $ as the dual graviton. In Bondi coordinates at future null infinity, we impose radiation fall-offs and fix a de Donder-like gauge together with an on-shell traceless condition, similarly to what happens in linearized gravity. Surface charges associated with the residual gauge transformations are constructed as boundary integrals via N\"other's 2-form. In $ D = 5 $, exploiting Hodge/Hodge-like decompositions on $ S^{3} $, the charge splits into a scalar sector $ Q_{\Phi} $, a vector sector $ Q_{V} $ and a TT sector $Q_{y^{\text{TT}}}$. $ Q_{\Phi} $ is parametrized by a single arbitrary scalar function $ \Phi $ (interpreted as the supertranslation-like parameter), $ Q_{V} $ is parametrized by a vector field $ V^{i} \in \mathfrak{Diff}(S^{3}) $ and the TT sector $Q_{y^{\text{TT}}}$ is parametrized by a trasverse-traceless rank-2 tensor $y_{ij}^{\text{TT}} \in \mathfrak{TT}(S^3)$. The corresponding charge algebra closes only if $V_i \in \mathfrak{o}(4)$ as semidirect sum generating an abelian extension of a $\mathfrak{BMS}$-like algebra featuring a higher-spin-like supertranslation sector.