Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2401.04523 |
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Sommario:
- Given a maximally symmetric $d$-dimensional background with isometry algebra $\mathfrak{g}$, a symmetric and traceless rank-$s$ field $ϕ_{a(s)}$ satisfying the massive Klein-Gordon equation furnishes a collection of massive $\mathfrak{g}$-representations with spins $j\in \{0,1,\cdots,s\}$. In this paper we construct the spin-$(s,j)$ projectors, which are operators that isolate the part of $ϕ_{a(s)}$ that furnishes the representation from this collection carrying spin $j$. In the case of an (anti-)de Sitter ((A)dS$_d$) background, we find that the poles of the projectors encode information about (partially-)massless representations, in agreement with observations made earlier in $d=3,4$. We then use these projectors to facilitate a systematic derivation of two-derivative actions with a propagating massless spin-$s$ mode. In addition to reproducing the massless spin-$s$ Fronsdal action, this analysis generates new actions possessing higher-depth gauge symmetry. In (A)dS$_d$ we also derive the action for a partially-massless spin-$s$ depth-$t$ field with $1\leq t \leq s$. The latter utilises the minimum number of auxiliary fields, and corresponds to the action originally proposed by Zinoviev after gauging away all Stückelberg fields. Some higher-derivative actions are also presented, and in $d=3$ are used to construct (i) generalised higher-spin Cotton tensors in (A)dS$_3$; and (ii) topologically-massive actions with higher-depth gauge symmetry. Finally, in four-dimensional $\mathcal{N}=1$ Minkowski superspace, we provide closed-form expressions for the analogous superprojectors.