Must be massive mass gap and singlet color

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Unformatted text preview: ent’’) A plausible picture of non-Abelian higher-spin gauge theory is summarized as follows.  High energy (unbroken symmetry): strong coupling  Low energy (broken symmetry): decoupling of massless higher spins ( no-go theorems All asymptotic higher-spin states must be massive and/ or invariant under higher-spin symmetries As one can see, perhaps the biggest difficulty with nonAbelian higher-spin gauge theory (with respect to its low-spin counterparts) is the absence of a phase with both unbroken symmetry and weak coupling (i.e., there is no analog of ultraviolet freedom for Yang-Mills theory, or infrared irrelevance for Einstein gravity), where the theory would be easier to study. 2. Dynamical symmetry breaking: Spin one versus higher spin The terminology ‘‘no-go theorem’’ assumes that the theorem (e.g., Coleman-Mandula’s) is formulated negatively as the impossibility of realizing some idea (e.g., the mixing of internal and spacetime symmetries) under some conditions. If the idea proves to be possible then, retrospectively, the no-go theorem is read positively (by contraposition) as the necessity of some property (e.g., supersymmetry) for the idea to work. Similarly, one can speculate that maybe S-matrix no-go theorems (Weinberg, 1964; Coleman and Mandula, 1967; Porrati, 2008) on massless higher-spin particles should be read positively as providing a hint (if not a proof) that, at the infrared scale where these theorems are valid, an exotic mechanism, reminiscent of mass gap and confinement in QCD, must necessarily take place in any higher-spin gauge theory. At low energy, higher-spin particles must either decouple from low-spin ones or acquire a mass: in both cases, asymptotic massless higher-spin states are unobservable. Note that, usually, the elusive higher-spin symmetry breaking Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 V. FULLY INTERACTING EXAMPLE: VASILIEV’S HIGHER-SPIN GRAVITY After repeating why a classically complete theory is key in higher-spin gravity, we lay out the salient features of Vasiliev’s approach leading to a class of models that is not only the arguably most natural one but also a potentially viable brewing pot for actual semirealistic models of quantum gravity. We finally address the ‘‘state of the art’’ and what we believe to be some ways forward. A. Examples of non-Abelian gauge theories It is not too much of an exaggeration to stress that the very existence of a fully interacting non-Abelian gauge field theory is a highly nontrivial fact, even at the classical level. Actually, looking to four spacetime dimensions, and focusing on bosonic gauge symmetries, notwithstanding the extreme 1000 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . importance that supersymmetry and matter couplings (which might be the same thing in higher-spin gravity) may play in order to have a phenomenologically viable model, one finds essentiall...
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This document was uploaded on 09/28/2013.

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