Made in amplitude calculations in ordinary

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Unformatted text preview: m field theory (Bern et al., 2007, 2009) as well as higher-spin gravity (Giombi and Yin, 2009, 2010), one may start raising criticism against the very assumptions behind the Fronsdal program: the higher-derivative nature of higher-spin interactions leads ultimately to a conceptual breakdown of the standard canonical approach to quantum field theory based on time slicing in ordinary spacetime. Although one can refer perturbatively to the canonical structure of the free fields (thought of as fluctuations around the spin-two background), the nonperturbative formulation of higher-spin symmetries leads toward an extension of spacetime by extra bosonic coordinates on which higher-spin translations act by linear differentiation. One may therefore think of a bosonic generalization of the superspace approach to supergravities, which is precisely what is provided by the unfolded dynamics program initiated by Vasiliev [for an illustration of the basic ideas in the context of higherspin supergravity, see, for example, Engquist, Sezgin, and Sundell (2003)]. IV. VARIOUS YES-GO EXAMPLES In this section we give a review of the various positive results obtained over the years concerning consistent higherspin cubic couplings in flat and AdS backgrounds. Section IV.A gathers together the results for cubic vertices in flat space, while Sec. IV.B essentially mentions the results obtained by Fradkin and Vasiliev in the late 1980s for cubic vertices in ðAÞdS4 . Section IV.C consists of a summary in the form of a general picture for non-Abelian higher-spin gauge theory, which seems to emerge from the known no-go theorems and yes-go examples. Of course, a word of caution should be added: the existence of consistent cubic couplings does not imply that a complete theory exists at all. However, the existence of full interacting equations (Vasiliev, 1990, 17 Including the Coleman-Mandula theorem, since the conserved charges used in its arguments depend on the asymptotic behavior of interactions at large distances. 18 See Eq. (B2) of Appendix B or Eq. (26) in Porrati (2008). Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 19 This criterion is subtle, however, since for nonvanishing Ã, generic spins cannot have as many gauge symmetries as for vanishing Ã. Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . TABLE I. s1 -s2 -s2 covariant vertices obtained by Berends, Burgers, and van Dam (1985). #s1 !s2 0 1 2 1 3 2 2 5 2 3 0 1 2 3 n                         1992, 2003) is a strong indication that a complete interacting Lagrangian20 may exist, at least in (A)dS background. Actually, one of the open problems in higher-spin gravity is whether or not the Fronsdal program can be pursued beyond the cubic order in a standard fashion. A. Consistent cubic vertices in Minkowski spacetime In the 1980s, the quest for high-spin interactions successfully started, taking flat spa...
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