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**Unformatted text preview: **os et al. (2007), and
Fotopoulos and Tsulaia (2007). It yields deformed Fronsdal
actions albeit with Abelian p-form-like vertices that do not
contain the non-Abelian interactions characteristic of the
higher-spin gravities to be discussed in this review.
Whether there exists a reﬁned limit in the spirit of the
aforementioned deconstruction by Sagnotti and Taronna
(2011), leading to such couplings, remains to be seen.
As far as the closed AdS string is concerned, it exhibits a
novel physical phenomenon that has no ﬂat-space analog,
whereby solitons, carrying quantum numbers of singletons,
are formed at cusps (Engquist and Sundell, 2006); in the
tensionless limit, their dynamics can be extracted by discretizing the Nambu-Goto action and degenerating spacetime to
the Dirac hypercone leading to a direct connection between
Vasiliev’s higher-spin gravities and tensionless closed strings
in which the graviton on both sides is identiﬁed (Engquist and
Sundell, 2006). The resulting physical picture is also in
accordance with the holographic proposals by Sundborg
(2001) and Sezgin and Sundell (2002b) later dubbed ‘‘la
grande bouffe’’ (Bianchi, Morales, and Samtleben, 2003).
Although these string-related theories are extremely interesting in their own right, here we are mainly concerned with
non-Abelian interactions for strictly massless ﬁelds in ﬂat
spacetime and for their (A)dS analogs with their critical
masses and the related higher-spin gravity.
In the case of strictly massless ﬁelds in ﬂat spacetime,
many S-matrix no-go theorems can be found in the literature
(Weinberg, 1964; Coleman and Mandula, 1967; Haag,
Lopuszanski, and Sohnius, 1975; Grisaru, Pendleton, and
van Nieuwenhuizen, 1977; Benincasa and Cachazo, 2007;
Porrati, 2008; Benincasa and Conde, 2011) that seemingly
forbid interacting massless higher-spin particles. Since the
relative strength of no-go theorems is measured by the weakness of their hypotheses, the S-matrix approach is usually
advertised because it does not require assumptions about
´
locality nor the Poincare-covariant realization of the incoming quanta. At a closer inspection, however, it turns out that
the S-matrix no-go results obtained so far concern only the
spin-s couplings involving s derivatives such as, for example,
two-derivative couplings between the graviton and other
ﬁelds.
If one accepts that the spin-s couplings contain more than s
derivatives, then these S-matrix arguments need to be reconsidered, and since the higher-spin interaction problem
presents itself already at the classical level, it is anyway
more satisfactory to pursue this analysis starting from purely
Lagrangian arguments. And indeed, numerous cubic vertices,
consistent at this order, have been found over the years in 990 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . Minkowski and (A)dS spacetimes. They all exhibit higherderivative couplings and will be reviewed here,...

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