Second quantizations g and gs expansions one must rst

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Unformatted text preview: cated understanding of their first quantizations (Ã and Ts expansions). Now to its advantage string theory offers a massless window where its first-quantization is weakly coupled, whereas in dealing with unbroken higherspin gravity one must face the whole packed-up content of its master fields. A striking similarity between open string theory and higher-spin gravities occurs when one considers (Konstein, Vasiliev, and Zaikin, 2000) extensions of the higher-spin algebra by an internal, associative algebra [see also Vasiliev (2004b, 2006)]. In such cases, there exist colored, massless spin-two fields resembling the spin-two states of open strings. These states can be given Chan-Paton factors since their interactions are based on an associative algebra. This similarity was pointed out by Francia and Sagnotti (2003, 2006) to which we refer the interested reader for related discussions. We note that the existence of colored gravitons in extended higher-spin theories does not enter in contradiction with the results of Boulanger et al. (2001), since there it was assumed that the fields considered could have spin two at most and the background was taken to be flat. At the classical level, the possibilities remain of having consistent truncations of closed-string theory down to higherspin gravity, and of higher-spin gravity down to general relativity. For example, both of these types of truncations may turn out to be relevant in the case of the hypothetical tensionless type-IIB closed-string theory on AdS5 Â S5 that should be the antiholographic dual of free four-dimensional maximally supersymmetric Yang-Mills theory in its 1=N expansion (Sundborg, 2001; Sezgin and Sundell, 2002b). Here the hypothetical five-dimensional maximally supersymmetric higher-spin gravity [for the linearized theory, see Sezgin and Sundell (2001b)] can be identified as the Kaluza-Klein reduction of the ‘‘bent’’ first Regge trajectory of the flat-space string theory (Bianchi, Morales, and Samtleben, 2003; Sezgin and Sundell, 2005). The full tensionless string theory then involves a much larger higher-spin symmetry algebra bringing in mixed-symmetry fields with critical masses such that they fit into multipletons (Bianchi, Morales, and Samtleben, 2003; Sezgin and Sundell, 2005). As for consistent truncations of higher-spin gravity down to possibly matter-coupled (super)gravities, a look at the state of affairs in gauged supergravities arising from sphere reductions (de Wit and Nicolai, 1987; Nastase, Vaman, and van Nieuwenhuizen, 1999; Cvetic et al., 2000) suggests that one Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 1003 should conjecture their existence in the case of maximal supersymmetry. As far as the type-IIB superstring is concerned, its graviton in ten-dimensional flat spacetime admits a deformation into a graviton of five-dimensional anti–de Sitter spacetime. More generally, a key physical effect of having a negative cosmological constant i...
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