Unformatted text preview: lts seem to apply in Minkowski
spacetime (Metsaev, 1991).
When the spin is unbounded, higher-spin interactions are
nonperturbatively nonlocal but perturbatively local, in the
rough sense that the number of derivatives is controlled by
the length scale. More precisely, at any ﬁnite order in the
power expansion in ‘ the vertices are local, but if all terms are
included, as usually required for consistency at the quartic
level, then the number of derivatives is unbounded.
Nonlocality: The number of derivatives is unbounded in
any perturbatively local vertex including an inﬁnite spectrum
of massless particles with unbounded spin.
The good news is that nonlocal theories do not automatically suffer from the higher-derivative problem. For nonlocal
theories that are perturbatively local, the problem can be
treated if the free theory is well behaved and if nonlocality
is cured perturbatively [see Simon (1990) for a comprehensive review on this point].
(iv) Massless higher-spin vertices are controlled by the
Concretely, in quantum ﬁeld theory computations where
massless particles are involved, one makes use of infrared and
ultraviolet cutoffs where ‘IR and ‘UV denote the corresponding length scales (‘UV ( ‘IR ). By deﬁnition of the cutoff
prescription, the typical wavelength of physical excitations ‘
(roughly, the ‘‘size of the laboratory’’) must be such that
‘UV < ‘ < ‘IR .
In low-spin physics, the ultraviolet scale is of the order of
the Planck length ‘UV $ ‘p , interactions are controlled by
that ultraviolet cutoff, and nonrenormalizable theories are
weakly coupled in the low-energy regime ‘ ) ‘p . In
higher-spin gauge theory, the situation is turned upside
down: interactions are controlled by the infrared cutoff
‘IRðhigher spinÞ (e.g., the AdS radius) and, since they are higher
derivative, the theory is strongly coupled in the high-energy
regime ‘ ( ‘IRðhigher spinÞ .
D. Higher-spin symmetry breakings While the transition from massless to massive higher-spin
particles is well understood at the tree level via the Stuckelberg
mechanism, the higher-spin symmetry breaking remains unknown at the interacting level. The qualitative scenario is Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . brieﬂy discussed in Sec. IV.D.1 and, ﬁnally, a tentative summary of the possible scenarios is presented in Sec. IV.D.2.
1. Higher-spin gauge symmetries are broken
at the infrared scale At energies of the order of the infrared cutoff for the
higher-spin gauge theory, i.e., when ‘ $ ‘IRðhigher spinÞ ,
higher-spin particles cannot be treated as ‘‘massless’’ any
more. Instead, they get a mass of the order of ‘À1higher spinÞ
and, consequently, the higher-spin gauge symmetries are
broken. Therefore, the no-go theorems do not apply any
more. Hence, low-spin physics can be recovered at energy
lower than the infrared...
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