**Unformatted text preview: **ds. Thinking of free
conformal scalar ﬁelds, the case of two dimensions is very
special, in that the stress tensor forms a closed operator
algebra (the Virasoro algebra). Indeed, already in three dimensions one encounters the full higher-spin current algebra
as one expands the operator product between two stress tensor
generators (including a scalar current rather than a central
term). Thus, in the case of four-dimensional theories of
quantum gravity, it seems that the simplest, most natural
procedure would be to start from Vasiliev-like higher-spin
gravities and then seek symmetry breaking mechanisms that
correspond to breaking the higher-spin currents, followed by
taking limits in which these decouple from operator product
expansions.
In fact, by putting more emphasis on the AdS/CFT correspondence, one provides further arguments (Girardello,
Porrati, and Zaffaroni, 2003) as to why higher-spin gravity
is a natural framework for seeking ultraviolet completions of
general relativity. Ordinary general relativity together with
various matter couplings (and without exotic vertices) may
then appear at low energies as the result of the dynamical
higher-spin symmetry breaking mechanism induced by radiative corrections proposed by Girardello, Porrati, and
Zaffaroni (2003), provided that the induced noncritical
mass gaps grow large at low energies. If so, higher-spin
gravity may bridge general relativity and string theory, which
might be needed ultimately in order to achieve nonperturbative unitarity. 24
Note that recently, in the AdS3 =CFT2 framework based on the
bulk theories provided by Blencowe (1989) and Prokushkin and
Vasiliev (1999), many interesting works appeared; see, e.g.,
Henneaux and Rey (2010), Campoleoni
et al. (2010),
Campoleoni, Fredenhagen, and Pfenninger (2011), Castro,
Lepage-Jutier, and Maloney (2011), Chang and Yin (2011),
Gaberdiel and Gopakumar (2011), Gaberdiel, Gopakumar,
Hartman, and Raju (2011), Gaberdiel, Gopakumar, and Saha
(2011), Gaberdiel and Hartman (2011), Gaberdiel and
Vollenweider (2011), Kraus and Perlmutter (2011), and references
therein. Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . E. Emergence of extended objects We now comment on the similarities and dissimilarities
between higher-spin gravity, with its double perturbative
expansion in terms of the dimensionless coupling g and the
cosmological constant Ã, and string theory, with its double
perturbative expansion in terms of the string coupling gs and
the string tension Ts . On the one hand, both of these theories
are genuine higher-derivative theories which implies that at
ﬁxed orders in g and gs , respectively, there are vertices with
ﬁelds of sufﬁciently high spins involving arbitrarily large
inverse powers of their massive parameters Ã and Ts , respectively. Thus, in order to understand their respective second
quantizations (g and gs expansions), one must ﬁrst obtain a
sufﬁciently sophisti...

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