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

TL;DR

The paper addresses how asymptotic symmetries and charges manifest for the Curtright (hook) field $\phi_{[\rho\sigma]\nu}$ in $D=5$, where the field is dual to the graviton. By fixing a de Donder-like gauge and imposing radiation-compatible fall-offs in Bondi coordinates, the authors solve residual gauge constraints with polyhomogeneous expansions and construct finite, boundary Noether charges from the leading boundary data of the field strength. In $D=5$ these charges split into a scalar sector $Q_{\Phi}$, a vector sector $Q_{V}$, and a TT sector $Q_{y^{TT}}$, forming a semidirect-sum algebra $\mathfrak{CBMS}(S^3)=\mathfrak{o}(4)\ltimes\bigl(C^{\infty}(S^3)\oplus\mathfrak{TT}(S^3)\bigr)$, a Curtright extension of the BMS-type symmetry with a higher-spin-like supertranslation. The work also discusses a possible missing scalar mode, outlines extensions to other mixed-symmetry fields, and suggests future links to duality, soft theorems, and memory effects in higher-spin gauge theories.

Abstract

This paper studies the asymptotic gauge charges of the Curtright mixed-symmetry rank-3 field $φ_{[ρσ]ν}$ 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_Φ $, a vector sector $ Q_{V} $ and a TT sector $Q_{y^{\text{TT}}}$. $ Q_Φ $ is parametrized by a single arbitrary scalar function $ Φ$ (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 $ \mathfrak{o}(4) \loplus (C^{\infty}(S^3) \oplus \mathfrak{TT}(S^3)) $, i.e an abelian extension of a $\mathfrak{BMS}$-like algebra featuring a higher-spin-like supertranslation sector.

Theorems & Definitions (6)

• Proposition 2.1: Off-shell identities of $H_{[\alpha\beta\gamma]\mu}$
• proof
• Proposition B.1
• proof
• Theorem B.2
• proof