Holography in 4D (super) higher spin theories and a test via cubic scalar couplings

By E. Sezgin, P. Sundell. 2003

398 citations recorded by the source corpus.

The correspondences proposed previously between higher spin gauge theories and free singleton fleld theories were recently extended into a more complete picture by Klebanov and Polyakov in the case of the minimal bosonic theory in D = 4 to include the strongly coupled flxed point of the 3d O(N) vector model. Here we propose an N = 1 supersymmetric version of this picture. We also elaborate on the role of parity in constrain- ing the bulk interactions, and in distinguishing two minimal bosonic models obtained as two difierent consistent truncations of the minimal N = 1 model that retain the scalar or the pseudo-scalar fleld. We refer to these models as the type-A and type-B models, respec- tively, and conjecture that the latter is holographically dual to the 3d Gross-Neveu model. In the case of the type-A model, we show the vanishing of the three-scalar amplitude with regular boundary conditions. This agrees with the O(N) vector model computation of Petkou, thereby providing a non-trivial test of the Klebanov-Polyakov conjecture.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d95f2cba3516c4f7f04e8f550ce3395cf1bde6bd

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In Nuclear and High Energy Physics

Citations in the corpus

The thermal free energy in large N Chern-Simons-matter theories (2012, methodology): “This duality is a generalization of the original conjectures [12, 13] relating the singlet sector of bosonic/fermionic vector models to the parity invariant Vasiliev’s theories.”
How higher-spin gravity surpasses the spin-two barrier (2010, methodology): “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 has been verified at the level of scalar cubic couplings in [129, 128], and more recently, at the general cubic level in [20”
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.”
Baryons, monopoles and dualities in Chern-Simons-matter theories (2015, background): “The U(N)k Chern-Simons-matter theories discussed above are conjectured [1, 2, 9, 3] (following the k = 0 case discussed in [4, 5]) to correspond to Vasiliev’s high-spin gravity theories on AdS4.”
On Higher Spin Gauge Theory and the Critical O(N) Model (2011, methodology): “(7)In this paper we have restricted our discussion to the type A minimal bosonic theory, in which the bulk scalar is parity even [4, 6].”
One loop tests of higher spin AdS/CFT (2013, background): “Similarly, 3-d theories of N massless fermion fields have been conjectured to be dual to Vasiliev’s type B theory, where the scalar has negative parity [10, 11].”
Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions (2012, background): “Indeed, it was suggested in [5, 6] (see also [7, 8, 9]) that the bosonic theories are dual to the type A high-spin gravity theories of Vasiliev [10], and the fermionic theories to the type B high-spin gravity theories of Vasiliev.”
d = 3 bosonic vector models coupled to Chern-Simons gauge theories (2011, background): “The gravity dual for this case was discussed in [44, 45], and it would be interesting to generalize our discussion of the theory with finite λ to this case.”
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 spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT (2014, neutral): “The original examples were for d = 3 [77–80] while generalizations to d > 3 were studied in [81, 82, 1, 2, 5, 6] (see also [83–86] for related work).”
Late-time structure of the Bunch-Davies de Sitter wavefunction (2014, background): “Interestingly, the cubic self-interaction of the conformally coupled scalar is absent in the classical Vasiliev equations [63, 64].”
Large \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 4 holography (2013, neutral): “However, starting with the work of Klebanov-Polyakov and others, a new class of AdS/CFT dualities [1, 2, 3, 4, 5, 6, 7] have been uncovered which do not obviously arise from any embedding in string theory.”
Spinning AdS propagators (2014, background): “More recently there has been a resurgence of higher spin gauge theories in AdS4 [2, 3, 4, 5], conjectured to be dual to three-dimensional CFTs like the O(N) vector model [6], the Gross-Neveu model [7] or certain large N Chern-Simons theories [8].”
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].”
The higher spin/vector model duality (2012, background): “The B-type minimal bosonic Vasiliev theory in AdS4, on the other hand, is conjectured by Sezgin and Sundell [2] to be dual to the fermionic version of the free and critical O(N) models.”