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**Unformatted text preview: **oni,
2003). 1004 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . VI. CONCLUSIONS AND OUTLOOK We discussed the key mechanism by which higher-spin
gravity evades the no-go theorems and, in particular, how the
equivalence principle is reconciled with higher-spin gauge
symmetry.
Starting in ﬂat spacetime, massless higher-spin particles
cannot be reconciled with the equivalence principle.
Nevertheless, the Weinberg-Witten theorem does not rule
out higher-derivative energy-momentum tensors made out
of higher-spin gauge ﬁelds. Hence massless higher-spin particles may couple nonminimally to a massless spin-two particle. However, in such a case the low-energy Weinberg
theorem rules out the self-coupled Einstein-Hilbert action
and minimally coupled matter, in particular, with low spins
(i.e., s ¼ 0, 1=2, and 1), in contradiction with observations.
Going to AdS spacetime, the Lorentz minimal coupling
reappears but only as a subleading term in a strongly coupled
derivative expansion. In order to do weakly coupled calculations, even at the cubic level for higher-spin gravity, one
thus needs a complete theory with the full derivative expansion under control. The simplest available candidate at the
moment is Vasiliev’s theory.
Remarkably, not only does it resolve all the difﬁculties
reported in the no-go theorems, but actually it also seems to
be the simplest unbroken higher-spin gravity in the sense that
it corresponds, via AdS/CFT, to a free conformal ﬁeld theory
with only scalar and/or fermion ﬁelds, albeit in large number.
Two major open problems that need to be considered are as
follows:
Can the Fronsdal program be pursued until quartic
vertices?
It is not totally excluded that the answer be ‘‘no’’ under
the requirement of perturbative locality. Moreover, scattering amplitudes in AdS can be deﬁned without using
an action principle, and the recent checks of the AdS/
CFT correspondence in the context of higher-spin
gravity at the cubic level were done by using the unfolded formalism in the bulk theory.
Does the dimensionless coupling in higher-spin gravity
become large at low energies in AdS?
If the answer is ‘‘yes’’ then higher-spin gravity is a
promising candidate for an effective quantum gravity
theory. Drawing on our experience with QCD, since
higher-spin gravity has been observed to be extremely
soft at high energy, it is tempting to think that the
coupling constant becomes weak in the ultraviolet and should grow in infrared, such that the dynamical
higher-spin symmetry breaking, which is present
already in the ultraviolet, gives rise to a ﬁnite mass
gap allowing the identiﬁcation of the low-energy and
low-spin regime.
ACKNOWLEDGMENTS We are grateful to S. Leclercq for collaborations on several
works closely related to this paper. We thank K. Alkalaev, G.
Barnich, A. Bengtsson, F. Buisseret, A. Campoleoni, N.
Colombo, P. P. Cook, V. Didenko, J. Engquist, D. Franc...

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