Abstract
Employing the world line spinning particle picture. We discuss the appearance of several different ‘gauges’ which we use to gain a deeper explanation of the Collective/Gravity identification. We discuss transformations and algebraic equivalences between them. For a bulk identification we develop a ‘gauge independent’ representation where all gauge constraints are eliminated. This ‘gauge reduction’ of Higher Spin Gravity demonstrates that the physical content of 4D AdS HS theory is represented by the dynamics of an unconstrained scalar field in 6d. It is in this gauge reduced form that HS Theory can be seen to be equivalent to a 3 + 3 dimensional bi-local collective representation of CFT3.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
W. Rarita and J. Schwinger, On a theory of particles with half integral spin, Phys. Rev. 60 (1941) 61 [INSPIRE].
C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D 18 (1978) 3624 [INSPIRE].
J. Fang and C. Fronsdal, Massless Fields with Half Integral Spin, Phys. Rev. D 18 (1978) 3630 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, Candidate to the Role of Higher Spin Symmetry, Annals Phys. 177 (1987) 63 [INSPIRE].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3+1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories in four-dimensions, three-dimensions and two-dimensions, Int. J. Mod. Phys. D 5 (1996) 763 [hep-th/9611024] [INSPIRE].
X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B 644 (2002) 303 [Erratum ibid. B 660 (2003) 403] [hep-th/0205131] [INSPIRE].
S. Giombi and X. Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].
A. Jevicki and B. Sakita, Collective Field Approach to the Large-N Limit: Euclidean Field Theories, Nucl. Phys. B 185 (1981) 89 [INSPIRE].
A. Jevicki and J. Yoon, Field Theory of Primaries in W N Minimal Models, JHEP 11 (2013) 060 [arXiv:1302.3851] [INSPIRE].
S.R. Das and A. Jevicki, Large-N collective fields and holography, Phys. Rev. D 68 (2003) 044011 [hep-th/0304093] [INSPIRE].
R. de Mello Koch, A. Jevicki, K. Jin and J.P. Rodrigues, AdS 4 /CFT 3 Construction from Collective Fields, Phys. Rev. D 83 (2011) 025006 [arXiv:1008.0633] [INSPIRE].
A. Jevicki, K. Jin and Q. Ye, Collective Dipole Model of AdS/CFT and Higher Spin Gravity, J. Phys. A 44 (2011) 465402 [arXiv:1106.3983] [INSPIRE].
A. Jevicki, K. Jin and J. Yoon, 1/N and Loop Corrections in Higher Spin AdS 4 /CFT 3 Duality, Phys. Rev. D 89 (2014) 085039 [arXiv:1401.3318] [INSPIRE].
R.R. Metsaev, Light cone form of field dynamics in Anti-de Sitter space-time and AdS/CFT correspondence, Nucl. Phys. B 563 (1999) 295 [hep-th/9906217] [INSPIRE].
S.J. Brodsky, G.F. de Tèramond and H.G. Dosch, QCD on the Light-Front - A Systematic Approach to Hadron Physics, Few Body Syst. 55 (2014) 407 [arXiv:1310.8648] [INSPIRE].
S.J. Brodsky, G.F. de Teramond, H.G. Dosch and J. Erlich, Light-Front Holographic QCD and Emerging Confinement, arXiv:1407.8131 [INSPIRE].
R.G. Leigh, O. Parrikar and A.B. Weiss, The Holographic Geometry of the Renormalization Group and Higher Spin Symmetries, Phys. Rev. D 89 (2014) 106012 [arXiv:1402.1430] [INSPIRE].
R.G. Leigh, O. Parrikar and A.B. Weiss, The Exact Renormalization Group and Higher-spin Holography, Phys. Rev. D 91 (2015) 026002 [arXiv:1407.4574] [INSPIRE].
L.A. Pando Zayas and C. Peng, Toward a Higher-Spin Dual of Interacting Field Theories, JHEP 10 (2013) 023 [arXiv:1303.6641] [INSPIRE].
M.R. Douglas, L. Mazzucato and S.S. Razamat, Holographic dual of free field theory, Phys. Rev. D 83 (2011) 071701 [arXiv:1011.4926] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
R. de Mello Koch, A. Jevicki, K. Jin, J.P. Rodrigues and Q. Ye, S=1 in O(N)/HS duality, Class. Quant. Grav. 30 (2013) 104005 [arXiv:1205.4117] [INSPIRE].
D. Das, S.R. Das, A. Jevicki and Q. Ye, Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence, JHEP 01 (2013) 107 [arXiv:1205.5776] [INSPIRE].
R. de Mello Koch, A. Jevicki, J.P. Rodrigues and J. Yoon, Canonical Formulation of O(N) Vector/Higher Spin Correspondence, arXiv:1408.4800 [INSPIRE].
S. Giombi and I.R. Klebanov, One Loop Tests of Higher Spin AdS/CFT, JHEP 12 (2013) 068 [arXiv:1308.2337] [INSPIRE].
S. Giombi, I.R. Klebanov and B.R. Safdi, Higher Spin AdS d+1 /CFT d at One Loop, Phys. Rev. D 89 (2014) 084004 [arXiv:1401.0825] [INSPIRE].
C. Fronsdal, Singletons and Massless, Integral Spin Fields on de Sitter Space (Elementary Particles in a Curved Space. 7., Phys. Rev. D 20 (1979) 848 [INSPIRE].
S.M. Kuzenko, S.L. Lyakhovich, A.Y. Segal and A.A. Sharapov, Anti-de Sitter spinning particle and two sphere, hep-th/9411162 [INSPIRE].
S.M. Kuzenko, S.L. Lyakhovich, A.Y. Segal and A.A. Sharapov, Massive spinning particle on anti-de Sitter space, Int. J. Mod. Phys. A 11 (1996) 3307 [hep-th/9509062] [INSPIRE].
P.S. Howe, S. Penati, M. Pernici and P.K. Townsend, Wave Equations for Arbitrary Spin From Quantization of the Extended Supersymmetric Spinning Particle, Phys. Lett. B 215 (1988) 555 [INSPIRE].
F. Bastianelli, O. Corradini and E. Latini, Spinning particles and higher spin fields on (A)dS backgrounds, JHEP 11 (2008) 054 [arXiv:0810.0188] [INSPIRE].
I.A. Bandos, J. Lukierski and D.P. Sorokin, Superparticle models with tensorial central charges, Phys. Rev. D 61 (2000) 045002 [hep-th/9904109] [INSPIRE].
I.A. Bandos, J. Lukierski, C. Preitschopf and D.P. Sorokin, OSp supergroup manifolds, superparticles and supertwistors, Phys. Rev. D 61 (2000) 065009 [hep-th/9907113] [INSPIRE].
V.E. Didenko and M.A. Vasiliev, Free field dynamics in the generalized AdS (super)space, J. Math. Phys. 45 (2004) 197 [hep-th/0301054] [INSPIRE].
G. Barnich and M. Grigoriev, Parent form for higher spin fields on anti-de Sitter space, JHEP 08 (2006) 013 [hep-th/0602166] [INSPIRE].
J.M. Bardeen, Gauge Invariant Cosmological Perturbations, Phys. Rev. D 22 (1980) 1882 [INSPIRE].
V.F. Mukhanov, H.A. Feldman and R.H. Brandenberger, Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions, Phys. Rept. 215 (1992) 203 [INSPIRE].
M.A. Vasiliev, Holography, Unfolding and Higher-Spin Theory, J. Phys. A 46 (2013) 214013 [arXiv:1203.5554] [INSPIRE].
M.A. Vasiliev, More on equations of motion for interacting massless fields of all spins in (3+1)-dimensions, Phys. Lett. B 285 (1992) 225 [INSPIRE].
M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [INSPIRE].
M.A. Vasiliev, Higher spin superalgebras in any dimension and their representations, JHEP 12 (2004) 046 [hep-th/0404124] [INSPIRE].
S. Giombi, I.R. Klebanov and A.A. Tseytlin, Partition Functions and Casimir Energies in Higher Spin AdS d+1 /CFT d , Phys. Rev. D 90 (2014) 024048 [arXiv:1402.5396] [INSPIRE].
M.A. Vasiliev, Higher-Spin Theory and Space-Time Metamorphoses, Lect. Notes Phys. 892 (2015) 227 [arXiv:1404.1948] [INSPIRE].
M.J. Strassler, Field theory without Feynman diagrams: One loop effective actions, Nucl. Phys. B 385 (1992) 145 [hep-ph/9205205] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1408.1255
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
de Mello Koch, R., Jevicki, A., Rodrigues, J.P. et al. Holography as a gauge phenomenon in Higher Spin duality. J. High Energ. Phys. 2015, 55 (2015). https://doi.org/10.1007/JHEP01(2015)055
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2015)055