RevModPhys.84.987

Looking at taylor expansions in other words vasilievs

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Unformatted text preview: gravity is essentially nonlocal in spacetime but admits a quasilocal formulation in terms of star products on the direct product of commutative spacetime and noncommutative twistor space, where one can then proceed building classical observables and geometries for the theory. This somewhat awkward albeit mathematically completely well-defined situation raises the issue of whether Vasiliev’s equations should be viewed as natural representative for higher-spin gravity or not? Since there are no other known examples of classes of higher-spin gravities with local degrees of freedom, it is difficult to make any direct comparisons. However, lessons can be drawn by looking at the AdS/ CFT correspondence. D. AdS/CFT correspondence: Vasiliev’s theory from free conformal fields In the previous sections we attempted to define a relation between the S matrix and Lagrangian approaches in the case of vanishing cosmological constant. Switching on the cosmological constant the notion of the S matrix becomes deformed into that of a holographic conformal field theory. Thus, one way of assessing to what extent a higher-spin gravity is ‘‘natural’’ is to ask oneself to what extent its dual conformal field theory is natural. 1002 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . Shortly after Maldacena’s version of the AdS/CFT conjecture, which was derived within a stringy context involving strong- and weak-coupling dual descriptions of branes, the question came as to what the antiholographic dual of a weakly coupled CFT could be. Since a free CFT has infinitely many conserved currents of arbitrary spin, in addition to the stressenergy tensor, it was natural to expect the AdS dual to be a higher-spin gauge theory containing a graviton. With a noticeable precursor (Bergshoeff et al., 1988), such ideas emerged progressively in a series of papers (Haggi-Mani and Sundborg, 2000; Konstein, Vasiliev, and Zaikin, 2000; Shaynkman and Vasiliev, 2001; Sundborg, 2001; Sezgin and Sundell, 2001a, 2002b, 2005; Witten, 2001; Klebanov and Polyakov, 2002; Mikhailov, 2002): the idea was born in the context of the type-IIB theory on AdS5 Â S5 (Haggi-Mani and Sundborg, 2000; Sezgin and Sundell, 2001a; Sundborg, 2001), and then pursued in a more general D-dimensional context, first at the level of kinematics (Konstein, Vasiliev, and Zaikin, 2000; Shaynkman and Vasiliev, 2001) and later at a dynamical level leading to the duality conjecture between a pure bosonic higher-spin gravity in any dimension and a theory of (a large number of) free conformal scalars in the vector representation of an internal symmetry group (Witten, 2001; Mikhailov, 2002; Sezgin and Sundell, 2002b), refined to include the strongly coupled fixed points of the threedimensional OðN Þ model and the Gross-Neveu model, in Klebanov and Polyakov (2002) and Sezgin and Sundell (2005), respectively. More precisely, the bilinear operators formed out o...
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