And sundell 2005 respectively more precisely the

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Unformatted text preview: f free fields couple to higher-spin sources identified as the boundary data of bulk higher-spin gauge fields. One should stress that although the boundary CFT is quadratic, it is nevertheless nontrivial since the bilinear operators actually couple to background sources; therefore the bulk dual theory is interacting. The concrete relation with Vasiliev’s unfolded equations in four and five dimensions was elaborated on by Sezgin and Sundell (2001a, 2002b, 2005), and the fully nonlinear bosonic higher-spin gravity in any dimension was then found in Vasiliev (2003). The agreement between Vasiliev’s four-dimensional higher-spin gravity and the sector of bilinear operators formed out of free conformal scalars and spinors in three dimensions was verified at the level of scalar cubic couplings by Petkou (2003) and Sezgin and Sundell (2005), and, more recently, at the general cubic level by Giombi and Yin (2009, 2010) under certain prescriptions which still remain to be spelled out in their entirety. Thus the question of whether Vasiliev’s higher-spin gravity is natural or not is equivalent to the question of whether free scalars (and spinors) are natural building blocks for three-dimensional conformal field theories with (unbroken or weakly broken) higher-spin currents. Or stated differently, thinking about Vasiliev’s higher-spin gravity is about as natural as thinking about threedimensional conformal field theories starting from free fields. Intermediate developments are given by Das and Jevicki (2003), Leigh and Petkou (2003), Leonhardt, Meziane, and Ruehl (2003), Bonelli (2004), Leonhardt and Ruehl (2004), Hartnoll and Prem Kumar (2005), Ruehl (2005), Diaz and Dorn (2006), Elitzur et al. (2007), and Yonge (2007). More recently, the full checks of the conjecture for AdS4 =CFT3 at the cubic level (Giombi and Yin, 2009, 2010) prompted a Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 revived interest in the correspondence.24 For instance, the conjecture was generalized in the presence of a ChernSimons gauge field on the three-dimensional boundary (Aharony, Gur-Ari, and Yacoby, 2011; Giombi et al., 2011). Another duality was proposed relating bosonic Vasiliev’s theory on de Sitter bulk spacetime dS4 and fermionic scalar fields Euclidean CFT3 (Anninos, Hartman, and Strominger, 2011). The thermodynamic behavior of Vasiliev’s higher-spin gravity was inferred from Conformal Field Theory computations (Shenker and Yin, 2011). Several attempts toward a constructive derivation of the bulk dual of a free CFT in the vector representation have been proposed, such as the bilocal field approach (Das and Jevicki, 2003; Jevicki, Jin, and Ye, 2011; Koch et al., 2011) and the renormalization group (Douglas, Mazzucato, and Razamat, 2010). Here we also stress that AdS/CFT is more to gauge field theory than what standard global-symmetry current algebra is to quantum field theory, essentially since the boundary currents are coupled to bulk gauge fiel...
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