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**Unformatted text preview: **ivative
expansion.
Taking higher-spin gravity seriously as a model for quantum gravity, the key issue is thus whether its loop corrections5, which are given in a weak-ﬁeld expansion more
reminiscent of the perturbative expansion of string theory
than that of general relativity, may generate masses dynamically for the higher-spin ﬁelds? Remarkably, relying on
arguments based on the anti–de Sitter/conformal ﬁeld
theory (AdS/CFT) correspondence (Girardello, Porrati, and
Zaffaroni, 2003), the answer seems afﬁrmative: the pattern of
symmetry breaking is similar in spirit to that of ordinary
quantum chromodynamics (QCD), with spin playing the
role of color, the metric playing the role of an Abelian gauge
ﬁeld, and the Goldstone modes being two-particle states; in
the leading order in perturbation theory, the spin-s ﬁeld
acquires mass for s > 2 while the spin-s À 1 Goldstone
mode is the lightest bound state (in its parity sector) between
the physical scalar and the massless spin-s À 2 particle. The
crucial missing ingredient is a ‘‘conﬁnement mechanism’’
that causes g to become large at low enough energies,
thus creating a mass gap leading to a low-energy effective
quantum gravity. 5 For related issues within the anti–de Sitter/conformal ﬁeld theory
(AdS/CFT) correspondence, see Klebanov and Polyakov (2002) and
Sezgin and Sundell (2002b) and the recent advances due to Giombi
and Yin (2009, 2010), which altogether point to the fact that fourdimensional higher-spin gravity should have a surprisingly simple
ultraviolet behavior as a quantum ﬁeld theory in anti–de Sitter
spacetime, in the sense that its boundary dual is weakly coupled
or even free, with a simple 1=N expansion. Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . Thus, the quantization of higher-spin gauge theories can
lead to interesting models providing deepened insights into
the interplay between quantum mechanics and geometry.
These might be of relevance not only in the high-energy limit
of quantum gravity and string theory, but also for providing
new ideas in observational physics, such as, for example, in
cosmology, where weakly coupled massless particles can
serve as dark matter candidates. Finally, the development of
the quantum theory of higher-spin ﬁelds may serve as a
source of inspiration for seeking and testing new methods
in quantum ﬁeld theory, such as the application of deformation and geometric quantizations as well as topological models to dynamical systems with local degrees of freedom.
Having provided all of these motivations for quantizing
higher-spin gauge ﬁelds, it is perhaps surprising to discover
that there is a drastic gap between Vasiliev’s on-shell approach to higher-spin gravity based on gauging a non-Abelian
global-symmetry algebra and the Fronsdal program: the latter
has so far been only partially completed, mainly at the cubic
level [for a recent discussion on this i...

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