Burgers and van dam 1986 deser and yang 1990 and is

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Unformatted text preview: l. Even more interesting, these currents can be obtained from some global invariances of the free theory by a Noether-like procedure, provided the constant parameters associated with these rigid symmetries be replaced by the gauge parameters of the spin-s1 field (also internal color indices must be treated appropriately) (Berends, Burgers, and van Dam, 1986; Deser and Yang, 1990). The simplest class of cubic interactions below the Bell-Robinson line is provided by the couplings between scalar fields (s2 ¼ 0) and a collection of higher-spin tensor gauge fields through the Berends–Burgers–van Dam currents containing s1 derivatives of the scalar fields (Berends, Burgers, and van Dam, 1986). Recently, they were reexamined by Bekaert (2006), Fotopoulos et al. (2007), and Bekaert, Joung, and Mourad (2009) as a toy model for higher-spin interactions. Note that these cubic interactions induce, at first order in the coupling constant, gauge transformations for the scalar field which are non-Abelian at second order and reproduce the group of unitary operators acting on free scalars on Minkowski spacetime (Bekaert, 2006; Bekaert, Joung, and Mourad, 2009). As demonstrated by Boulanger, Leclercq, and Sundell (2008), in a flat background the non-Abelian 2-s-s vertex is unique and involves a total number of 2s À 2 derivatives. From s ¼ 3 on, the non-Abelian 2-s-s vertex in Minkowski spacetime is thus ‘‘nonminimal’’ and the full Lagrangian (if any) has no chance of being diffeomorphism invariant, a fact explicitly shown by Boulanger and Leclercq (2006) and Boulanger, Leclercq, and Sundell (2008). It was also shown by Boulanger, Leclercq, and Sundell (2008) that the unique and non-Abelian 2-s-s vertex in Minkowski spacetime is nothing but the leading term in the flat limit of the corresponding AdS Fradkin-Vasiliev vertex that, among others, contains the Lorentz minimal coupling. That the minimal Lorentz coupling term in the Fradkin-Vasiliev vertex is subleading in the flat limit shows that the Weinberg equivalence principle is restored for higher spins in AdS spacetime but is lost in the flat limit. This supports the need to consider higherspin interactions in the AdS background, at least if one wants to make a contact between higher-spin gauge fields and lowspin theories including Einstein-Hilbert gravity. 21 Note that one can trivially write down higher-derivative BornInfeld–like consistent cubic interactions involving only gaugeinvariant linearized field-strength tensors (Damour and Deser, 1987). However, these interactions deform neither the gauge algebra nor the gauge transformations at first order in some coupling constant. Nevertheless, they might be needed when pushing the non-Abelian cubic vertices to the next order in the coupling constants. 996 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . Recently, general results on the structure of cubic s-s0 -s00 couplings (s s0 s...
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This document was uploaded on 09/28/2013.

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