Hence low spin physics can be recovered at energy

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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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