Discussion on this issue see eg bengtsson 2008 and

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Unformatted text preview: ssue, see, e.g., Bengtsson (2008) and references therein]. Hence a key question6 is whether the Fronsdal program can be completed at the quartic level, even in the case of the aforementioned minimal bosonic model? This apparently straightforward problem will keep a number of interesting surprises in store, in particular, in view of the aforementioned properties of the AdS/CFT correspondence (Sezgin and Sundell, 2002b; Giombi and Yin, 2009, 2010) which have been derived using a rather different approach, as we return to in Sec. V and summarize in Sec. VI. As far as more general interacting quantum field theories with higher-spin fields are concerned, open string field theory in flat spacetime provides a basic example thereof albeit with a massless sector restricted to spins less than or equal to 1. Recently, motivated by the similarities between open string theory and higher-spin gravities mainly at the level of free fields (Francia and Sagnotti, 2003, 2006), Sagnotti and Taronna (2011) deconstructed its first Regge trajectory and arrived at the germs of the non-Abelian interactions for massless totally symmetric tensors in flat spacetime (Boulanger and Leclercq, 2006; Boulanger, Leclercq, and Sundell, 2008) whose deformations into (A)dS spacetimes (Boulanger, Leclercq, and Sundell, 2008) lead to the FradkinVasiliev cubic vertices. Moreover, Polyakov (2009) proposed to extend the open superstring in flat spacetime by sectors of states with novel world-sheet ghost numbers containing massless higher-spin particles in interaction. He also managed to show (Polyakov, 2010) that these higher-spin states 6 Here we want to stress that it is only by closing the quartic order that the cubic Lagrangian, including cubic curvature couplings known as cubic Born-Infeld terms, will be completely fixed (if it exists). Because of the double perturbative expansion, the BornInfeld couplings dominate over the minimal couplings in physical amplitudes (assuming a deformed Fronsdal action with finite BornInfeld ‘‘tail’’) and hence the quartic-closure problem must be addressed prior to any attempts to do physics with incomplete cubic actions. In other words, analyses based solely on current exchange may receive large corrections due to the exotic usage of the cosmological constant. Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 989 interact with the closed-string graviton and that these interactions reproduce the aforementioned germs of Boulanger and Leclercq (2006) and Boulanger, Leclercq, and Sundell (2008). As far as actual tensionless limits of strings are concerned, there is a vast literature which we cannot cover here. Of the various results that have been obtained, we simply point to the rather drastic difference between tensionless limits of, on the one hand, the open string in flat space and, on the other hand, the closed string in anti–de Sitter spacetime. A precise version of the former was taken by Bonelli (2003), Buchbinder et al. (2006), Fotopoul...
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