Higher spin gauge theory and holography: the three-point functions

By S. Giombi, Xi Yin. 2009

476 citations recorded by the source corpus.

In this paper we calculate the tree level three-point functi ons of Vasiliev’s higher spin gauge theory in AdS4 and find agreement with the correlators of the free field theory of N massless scalars in three dimensions in the O(N) singlet sector. This provides substantial evidence that Vasiliev theory is dual to the fre e field theory, thus verifying a conjecture of Klebanov and Polyakov. We also find agreement with the critical O(N) vector model, when the bulk scalar field is subject to the alternative boundary condition such that its dual operator has classical dimension 2.

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

View Paper: https://www.semanticscholar.org/paper/ffa7f78c151dfd994d2b43fe1ce42b37df73e46c

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Citations in the corpus

What Can Gauge-Gravity Duality Teach Us about Condensed Matter Physics? (2011, background): “Strong evidence for such a duality has also appeared for CFTs without any supersymmetry [6, 7].”
ABJ triality: from higher spin fields to strings (2012, methodology): “The corresponding boundary-to-bulk propagator is computed in [4].”
Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory (2012, methodology): “The computations of [18,19] were quite involved with a simple result in the end, moreover some ambiguities to be resolved have been observed at the intermediate steps.”
On the uniqueness of higher-spin symmetries in AdS and CFT (2013, methodology): “4) is totally fixed by the HS symmetry and does not require the knowledge of the full HS theory in AdS, see [75–78] for examples of computations, which are much simpler than the perturbative computations in Vasiliev theory [79,80].”
On the tensionless limit of string theory, off-shell higher spin interaction vertices and BCFW recursion relations (2010, background): “These results, apart form being remarkable in their own right, can also be extremely useful for a better understanding of String/M theory in particular in the context of AdS/CFT correspondence [78–85].”
AdS description of induced higher-spin gauge theory (2013, background): “in [21] satisfy the ordinary ∆+ boundary conditions, corresponding to γs = 0 in (7.”
Scalar fields and three-point functions in D = 3 higher spin gravity (2011, background): “This proposal was studied early on in [11,12,13], as well as in the recent papers [14,15,16,17,18].”
Quartic AdS interactions in higher-spin gravity from Conformal Field Theory (2015, methodology): “So far only the cubic interactions have been extracted in explicit form from Vasiliev’s equations [40, 48, 49, 52, 69, 70].”
An AdS_3 Dual for Minimal Model CFTs (2010, background): “…1, 1, 0N−4]⊕ [0N−3, 1, 2]⊕ 2 · [2, 0N−3, 1]⊕ [0N−3, 2, 0] ⊕ 5 · [0, 1, 0N−4, 1]⊕ 4 · [1, 0N−2] , (C.9) and H(n=0) [0,1,0N−3] = [0, 1, 0N−3] (C.10) H(n=1) [0,1,0N−3] = [2, 0N−2]⊕ [0N−3, 1, 1]⊕ [0, 1, 0N−3] (C.11) H(n=2) [0,1,0N−3] = [1, 1, 0N−4, 1]⊕ [2, 0N−2]⊕ 2 · [0N−3, 1, 1]⊕ 3 · [0, 1, 0N−3] .”
Partition functions of higher spin black holes and their CFT duals (2011, background): “Relatively recently, it has been realized that higher spin theories may lead to soluble examples of the AdS/CFT correspondence [3,4,5,6,7,8,9,10,11,12,13,14,15,16].”
Minimal model holography (2012, result): “Recall that this was the compelling piece of evidence [67, 68] for the Klebanov–Polyakov proposal for AdS4/CFT3 [90] and its generalizations [106]; see also [109, 118, 97, 105] for earlier work.”
A note on CFT correlators in three dimensions (2011, background): “Strong evidences in support of these dualities have been found recently [5, 6], and a computable framework has been formulated which allows one to compare the boundary and bulk order by order in the 1/N expansion.”
Averaged null energy condition from causality (2016, background): “ic, traceless spin-scurrent in the 33 theory of a free scalar takes the form X u u= Xs i=0 as i :(@ u) i˚(@ u) s i˚: (C.1) where as i are known coecients. (The explicit formula is equation (4.99) in [43] but will not be needed.) Therefore after integration by parts, the generalization of the average”
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].”
DE SITTER MUSINGS (2012, unknown): “The proposal, which is inspired by similar efforts for the AdS version of higher spin gravity [110, 111, 112, 113, 114, 115], is that the conformal field theory is simply a free theory of N scalar fields φa transforming as an Sp(N) vector.”