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**Unformatted text preview: **ent’’)
A plausible picture of non-Abelian higher-spin gauge theory
is summarized as follows.
High energy (unbroken symmetry): strong coupling
Low energy (broken symmetry): decoupling of massless
higher spins ( no-go theorems
All asymptotic higher-spin states must be massive and/
or invariant under higher-spin symmetries
As one can see, perhaps the biggest difﬁculty with nonAbelian higher-spin gauge theory (with respect to its low-spin
counterparts) is the absence of a phase with both unbroken
symmetry and weak coupling (i.e., there is no analog of
ultraviolet freedom for Yang-Mills theory, or infrared irrelevance for Einstein gravity), where the theory would be easier
to study. 2. Dynamical symmetry breaking: Spin one versus higher spin The terminology ‘‘no-go theorem’’ assumes that the theorem (e.g., Coleman-Mandula’s) is formulated negatively as
the impossibility of realizing some idea (e.g., the mixing of
internal and spacetime symmetries) under some conditions. If
the idea proves to be possible then, retrospectively, the no-go
theorem is read positively (by contraposition) as the necessity
of some property (e.g., supersymmetry) for the idea to work.
Similarly, one can speculate that maybe S-matrix no-go
theorems (Weinberg, 1964; Coleman and Mandula, 1967;
Porrati, 2008) on massless higher-spin particles should be
read positively as providing a hint (if not a proof) that, at the
infrared scale where these theorems are valid, an exotic
mechanism, reminiscent of mass gap and conﬁnement in
QCD, must necessarily take place in any higher-spin gauge
theory. At low energy, higher-spin particles must either decouple from low-spin ones or acquire a mass: in both cases,
asymptotic massless higher-spin states are unobservable.
Note that, usually, the elusive higher-spin symmetry breaking
Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 V. FULLY INTERACTING EXAMPLE:
VASILIEV’S HIGHER-SPIN GRAVITY After repeating why a classically complete theory is key in
higher-spin gravity, we lay out the salient features of
Vasiliev’s approach leading to a class of models that is not
only the arguably most natural one but also a potentially
viable brewing pot for actual semirealistic models of quantum
gravity. We ﬁnally address the ‘‘state of the art’’ and what we
believe to be some ways forward.
A. Examples of non-Abelian gauge theories It is not too much of an exaggeration to stress that the very
existence of a fully interacting non-Abelian gauge ﬁeld theory is a highly nontrivial fact, even at the classical level.
Actually, looking to four spacetime dimensions, and focusing
on bosonic gauge symmetries, notwithstanding the extreme 1000 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . importance that supersymmetry and matter couplings (which
might be the same thing in higher-spin gravity) may play in
order to have a phenomenologically viable model, one ﬁnds
essentiall...

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