# On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory - High Energy Physics - Theory

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Abstract: We address the uniqueness of the minimal couplings between higher-spin fieldsand gravity. These couplings are cubic vertices built from gauge non-invariantconnections that induce non-abelian deformations of the gauge algebra. We showthat Fradkin-Vasiliev-s cubic 2-s-s vertex, which contains up to 2s-2derivatives dressed by a cosmological constant $\Lambda$, has a limit where:{i} $\Lambda\to 0$; {ii} the spin-2 Weyl tensor scales{\emph{non-uniformly}} with s; and {iii} all lower-derivative couplings arescaled away. For s=3 the limit yields the unique non-abelian spin 2-3-3 vertexfound recently by two of the authors, thereby proving the \emph{uniqueness} ofthe corresponding FV vertex. We extend the analysis to s=4 and a class of spin1-s-s vertices. The non-universality of the flat limit high-lightens not onlythe problematic aspects of higher-spin interactions with $\Lambda=0$ but alsothe strongly coupled nature of the derivative expansion of the fully nonlinearhigher-spin field equations with $\L eq 0$, wherein the standard minimalcouplings mediated via the Lorentz connection are \emph{subleading} at energyscales $\sqrt{|\Lambda|}<< E<< M { m p}$. Finally, combining our results withthose obtained by Metsaev, we give the complete list of \emph{all} themanifestly covariant cubic couplings of the form 1-s-s and 2-s-s, in Minkowskibackground.

Autor: Nicolas Boulanger, Serge Leclercq, Per Sundell

Fuente: https://arxiv.org/