Notes On Higher Spin Symmetries

By A. Mikhailov. 2002

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The strong form of the AdS/CFT correspondence implies that the leading $N$ expressions for the connected correlation functions of the gauge invariant operators in the free ${\cal N}=4$ supersymmetric Yang-Mills theory with the gauge group SU(N) correspond to the boundary S matrix of the classical interacting theory in the Anti de Sitter space. It was conjectured recently that the theory in the bulk should be a local theory of infinitely many higher spin fields. In this paper we study the free higher spin fields ($N=\infty$) corresponding to the free scalar fields on the boundary. We explicitly construct the boundary to bulk propagator for the higher spin fields and show that the classical solutions in the bulk are in one to one correspondence with the deformations of the free action on the boundary by the bilinear operators. We also discuss the constraints on the correlation functions following from the higher spin symmetry. We show that the higher spin symmetries fix the correlation functions up to the finite number of parameters. We formulate sufficient conditions for the bulk theory to reproduce the free field correlation functions on the boundary.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1e3569133aac83e7a245fc904ae2a1b780e189ce

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Citations in the corpus

Black holes in three dimensional higher spin gravity: a review (2012, background): “An impressive amount of evidence for the duality has been obtained in recent years [24,25,26,27,28,29,30], including the calculation of three point functions in the bulk [31,32,33].”
Higher symmetries of the laplacian (2002, background): “The motivation for this article comes from physics, especially the recent theory of higher spin fields and their symmetries: see [ 32 , 37, 38] and references therein.”
Higher order singletons, partially massless fields and their boundary values in the ambient approach (2013, background): “In agreement with the holographic picture, most of the struc tures underlying totally symmetric higher-spin (HS) gauge fields around an anti de Sitter (AdS) background are determined by those of a scalar singleton – the conformal scalar fie ld living on the conformal boundary [1, 2, 3].”
Higher Spin Symmetry and N = 4 SYM (2004, unknown): “†nbeisert@aei.mpg.de ‡Massimo.Bianchi@roma2.infn.it §Francisco.Morales@lnf.infn.it ¶Henning.Samtleben@desy.de”
Bounding scalar operator dimensions in 4D CFT (2008, background): “extra bilinear in ˚terms denoted by ... make the operator conserved for l>0 (in accord with the unitarity bounds (3.3)), without disturbing the tracelessness. Their exact form can be found e.g. in [23]. In particular, there is of course the dimension 2 scalar O 2;0 = 1 p 2 ˚2 ; where the constant”
Quartic AdS interactions in higher-spin gravity from Conformal Field Theory (2015, background): “where Fs(x, u,∇, ∂u) is the Fronsdal operator [78,81] Fs(x, u,∇, ∂u) = −m(2)s − u(2)(∂u · ∂u)− (u · ∇) ( (∇ · ∂u)− 1 2 (u · ∇)(∂u · ∂u) ) , (2.”
Higher spin black holes (2011, background): “Introduction Theories of gravity coupled to massless higher spin fields [1,2,3,4,5] have received increased attention in recent years due to their appearance within the AdS/CFT correspondence [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21].”
A relation between approaches to integrability in superconformal Yang-Mills theory (2003, unknown): “6 in [29]) c (j−2) k = (−1) /k!(2)(j − k − 2)!(2).”
Higher spin black holes from CFT (2012, background): “Higher spin theories of gravity in Anti de Sitter space, with massless gauge fields of spin s > 2 in addition to the graviton, are dual to field theories with extended conformal invariance [1, 2, 3, 4, 5, 6].”
The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory (2003, background): “e planar one-loop Hamiltonian. It might turn out to be a consequence of integrability. One might also speculate that it is some remnant of the broken higher spin symmetry of the free theory, see e.g. [52,53,54] and references in [49]. 5 Subsectors Especially in view of some recent advances of the Ad”
On conformal Killing symmetric tensor fields on Riemannian manifolds (2011, background): “ng vector (covector) ﬁelds are the classic object of the Riemannian geometry. Conformal Killing symmetric tensor ﬁelds of higher rank naturally appear in various problems of physics and geometry (see [21, 7, 8, 13, 20, 6, 1]). There are also many papers where antisymmetric conformal Killing tensor ﬁ”
Thermodynamics of higher spin black holes in 3D (2012, background): “In weakly interacting limits large-N field theories have been argued to be dual to higher spin theories of gravity in AdS spacetimes [7, 8, 9, 10, 11].”
Higher spin gauge theory and holography: the three-point functions (2009, methodology): “It is far from obvious, a priori, that the assumption of [27] that the three point functions have the same structure as in free field theory, holds for the currents in Vasiliev theory.”
AdS dual of the critical O(N) vector model (2002, methodology): “In particular, it was proposed that the massless higher-spin gauge theory with N = 8 supersymmetry in AdS5 is closely related to the free N = 4 large N SYM theory [11, 12, 15, 16, 18].”