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 ${\varphi }_{[\rho \sigma ]\nu }$ 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 Nöther'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.

Published version in JPhysA