**Unformatted text preview: **cutoff of higher-spin gauge theory
‘ > ‘IRðhigher spinÞ .
In Minkwoski spacetime, a natural infrared scale of massless higher-spin particles is the ultraviolet scale of low-spin
physics: ‘IRðhigher spinÞ $ ‘UVðlow spinÞ $ ‘p . Then the corresponding massive higher-spin particles have masses not
smaller than the Planck mass and the higher-spin interactions
become ‘‘irrelevant’’ in the low-energy (sub-Planckian) regime. By naive dimensional analysis, in the high-energy
(trans-Planckian) regime the scattering amplitudes should
diverge since the theory is not (power-counting) renormalizable. However, for an inﬁnite tower of higher-spin particles,
the total scattering amplitudes may be extremely soft, or even
ﬁnite. These possibilities are realized for tensile string theory
around Minkowski spacetime where the ultraviolet scale is
the string length ‘UVðstringÞ $ ‘s , which is usually taken to be
of the order of the ultraviolet scale for gravity ‘s $ ‘p . The
underlying symmetry principle behind such a phenomenon
remains unknown, although the standard lore is that higherspin symmetries play a key role in its understanding.
In AdS spacetime, the situation is drastically different because the natural infrared scale is the radius of curvature
‘IRðhigherspinÞ $ RAdS $ À1 and the ultraviolet scale may remain
the Planck length ‘UVðhigher spinÞ $ ‘p . The high-energy limit of
higher-spin gauge theory is then equivalent to the ﬂat limit
‘ ( RAdS . The Fradkin-Vasiliev cubic vertices and Vasiliev
full nonlinear equations are precisely along these lines. 999 is presented as a ‘‘spontaneous’’ symmetry breaking such
as the Brout-Englert-Higgs mechanism in the electroweak
theory, but pursuing the analogy with QCD might be fruitful
and one might think of a ‘‘dynamical’’ symmetry breaking
where the Goldstone modes would be composite ﬁelds. From
holographic arguments, Girardello, Porrati, and Zaffaroni
(2003) indeed advocated for such a scenario whereby masses
for all (even) higher-spin ﬁelds in Vasiliev’s minimal theory
in AdS4 are generated by quantum one-loop corrections while
all low-spin gauge ﬁelds remain massless. We stress the direct
similarity to the Schwinger mechanism in two-dimensional
quantum electrodynamics (Schwinger, 1962) and the reminiscence to the saturation proposals for mass generation in
three- and four-dimensional pure QCD; see, e.g., Aguilar and
Papavassiliou (2008) and Aguilar, Binosi, and Papavassiliou
(2010), and references therein.
A way to present a summary of the two phases of higherspin gauge theory is by analogy with non-Abelian Yang-Mills
theory (say quarkless QCD) whose main properties are listed
as follows.
High energy (unbroken symmetry): weak coupling
(‘‘asymptotic freedom’’)
Low energy (broken symmetry): strong coupling ) nonperturbative effects
All asymptotic states must be massive (‘‘mass gap’’) and
singlet (‘‘color conﬁnem...

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