Abstract
We determine the boundary terms of the free higher-spin action which reproduce the AdS Fronsdal equations in an AdS manifold with a finite distance boundary. The boundary terms are further constrained by the gauge invariance of the total action. We show that, for spins larger than two, no local boundary term can restore the full gauge symmetry, and the broken symmetry corresponds to higher-spin Weyl transformations on the boundary CFT. The boundary action is used for the evaluation of the on-shell higher-spin AdS action in terms of the boundary data given by a conformal higher-spin field.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Argurio, G. Barnich, G. Bonelli and M. Grigoriev eds., Higher-Spin Gauge Theories, in proceedings of First Solvay Workshop, Brussels, 12-14 May 2004, International Solvay Institutes for Physics and Chemistry (2006) [http://www.ulb.ac.be/sciences/ptm/pmif/Solvay1proc.pdf].
M. Bianchi and V. Didenko, Massive higher spin multiplets and holography, hep-th/0502220 [INSPIRE].
D. Francia and C. Hull, Higher-spin gauge fields and duality, hep-th/0501236 [INSPIRE].
N. Bouatta, G. Compere and A. Sagnotti, An Introduction to free higher-spin fields, hep-th/0409068 [INSPIRE].
X. Bekaert, S. Cnockaert, C. Iazeolla and M. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [INSPIRE].
A. Sagnotti, E. Sezgin and P. Sundell, On higher spins with a strong Sp(2,R) condition, hep-th/0501156 [INSPIRE].
D. Sorokin, Introduction to the classical theory of higher spins, AIP Conf. Proc. 767 (2005) 172 [hep-th/0405069] [INSPIRE].
D. Francia and A. Sagnotti, Higher-spin geometry and string theory, J. Phys. Conf. Ser. 33 (2006) 57 [hep-th/0601199] [INSPIRE].
X. Bekaert, N. Boulanger and P. Sundell, How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples, arXiv:1007.0435 [INSPIRE].
A. Sagnotti, Notes on Strings and Higher Spins, arXiv:1112.4285 [INSPIRE].
G. Bonelli, On the covariant quantization of tensionless bosonic strings in AdS space-time, JHEP 11 (2003) 028 [hep-th/0309222] [INSPIRE].
G. Bonelli, On the boundary gauge dual of closed tensionless free strings in AdS, JHEP 11 (2004) 059 [hep-th/0407144] [INSPIRE].
D. Polyakov, Interactions of Massless Higher Spin Fields From String Theory, Phys. Rev. D 82 (2010) 066005 [arXiv:0910.5338] [INSPIRE].
D. Polyakov, Gravitational Couplings of Higher Spins from String Theory, Int. J. Mod. Phys. A 25 (2010) 4623 [arXiv:1005.5512] [INSPIRE].
D. Polyakov, Higher Spins and Open Strings: Quartic Interactions, Phys. Rev. D 83 (2011) 046005 [arXiv:1011.0353] [INSPIRE].
D. Polyakov, A String Model for AdS Gravity and Higher Spins, Phys. Rev. D 84 (2011) 126004 [arXiv:1106.1558] [INSPIRE].
A. Sagnotti and M. Taronna, String Lessons for Higher-Spin Interactions, Nucl. Phys. B 842 (2011)299 [arXiv:1006.5242] [INSPIRE].
B. Sundborg, Stringy gravity, interacting tensionless strings and massless higher spins, Nucl. Phys. Proc. Suppl. 102 (2001) 113 [hep-th/0103247] [INSPIRE].
E. Witten, Spacetime Reconstruction, talk given at J.H. Schwarz 60 th Birthday Conference, Cal Tech, 2-3 November 2001 [http://theory.caltech.edu/jhs60/witten/1.html].
A. Mikhailov, Notes on higher spin symmetries, hep-th/0201019 [INSPIRE].
A.A. Tseytlin, On limits of superstring in AdS 5 × S 5, Theor. Math. Phys. 133 (2002) 1376 [hep-th/0201112] [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].
A.Y. Segal, Conformal higher spin theory, Nucl. Phys. B 664 (2003) 59 [hep-th/0207212] [INSPIRE].
I. Klebanov and A. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining Conformal Field Theories with A Higher Spin Symmetry, arXiv:1112.1016 [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
M. Vasiliev, Higher spin gauge theories in any dimension, Comptes Rendus Physique 5 (2004) 1101 [hep-th/0409260] [INSPIRE].
M. Vasiliev, Higher spin gauge theories in various dimensions, Fortsch. Phys. 52 (2004) 702 [hep-th/0401177] [INSPIRE].
L. Girardello, M. Porrati and A. Zaffaroni, 3 − D interacting CFTs and generalized Higgs phenomenon in higher spin theories on AdS, Phys. Lett. B 561 (2003) 289 [hep-th/0212181] [INSPIRE].
E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040] [INSPIRE].
A.C. Petkou, Evaluating the AdS dual of the critical O(N) vector model, JHEP 03 (2003) 049 [hep-th/0302063] [INSPIRE].
A.C. Petkou, Holography, duality and higher-spin theories, hep-th/0410116 [INSPIRE].
R. Manvelyan and W. Rühl, The Masses of gauge fields in higher spin field theory on the bulk of AdS 4, Phys. Lett. B 613 (2005) 197 [hep-th/0412252] [INSPIRE].
R. Manvelyan and W. Rühl, The Off-shell behaviour of propagators and the Goldstone field in higher spin gauge theory on AdS d+1 space, Nucl. Phys. B 717 (2005) 3 [hep-th/0502123] [INSPIRE].
R. Manvelyan and W. Rühl, The Quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of AdS 4, Nucl. Phys. B 733 (2006) 104 [hep-th/0506185] [INSPIRE].
R. Manvelyan and W. Rühl, The Structure of the trace anomaly of higher spin conformal currents in the bulk of AdS 4, Nucl. Phys. B 751 (2006) 285 [hep-th/0602067] [INSPIRE].
R. Manvelyan, K. Mkrtchyan and W. Rühl, Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization, Nucl. Phys. B 803 (2008) 405 [arXiv:0804.1211] [INSPIRE].
R. Metsaev, Shadows, currents and AdS, Phys. Rev. D 78 (2008) 106010 [arXiv:0805.3472] [INSPIRE].
R. Metsaev, Gauge invariant two-point vertices of shadow fields, AdS/CFT and conformal fields, Phys. Rev. D 81 (2010) 106002 [arXiv:0907.4678] [INSPIRE].
S. Giombi and X. Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].
S. Giombi and X. Yin, Higher Spins in AdS and Twistorial Holography, JHEP 04 (2011) 086 [arXiv:1004.3736] [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [INSPIRE].
M. Henneaux and S.-J. Rey, Nonlinear W infinity as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [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].
X. Bekaert, E. Joung and J. Mourad, Effective action in a higher-spin background, JHEP 02 (2011) 048 [arXiv:1012.2103] [INSPIRE].
J.W. York, Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [INSPIRE].
G. Gibbons and S. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
E. Fradkin and A.A. Tseytlin, Conformal supergravity, Phys. Rept. 119 (1985) 233 [INSPIRE].
E. Fradkin and V.Y. Linetsky, Cubic interaction in conformal theory of integer higher spin fields in four-dimensional space-time, Phys. Lett. B 231 (1989) 97 [INSPIRE].
E. Fradkin and V.Y. Linetsky, Conformally invariant field theory with higher spins, Sov. Phys. Dokl. 35 (1990) 256 [INSPIRE].
D. Francia and A. Sagnotti, Minimal local Lagrangians for higher-spin geometry, Phys. Lett. B 624 (2005) 93 [hep-th/0507144] [INSPIRE].
D. Francia, J. Mourad and A. Sagnotti, Current Exchanges and Unconstrained Higher Spins, Nucl. Phys. B 773 (2007) 203 [hep-th/0701163] [INSPIRE].
D. Francia, J. Mourad and A. Sagnotti, (A)dS exchanges and partially-massless higher spins, Nucl. Phys. B 804 (2008) 383 [arXiv:0803.3832] [INSPIRE].
M. Vasiliev, Cubic Vertices for Symmetric Higher-Spin Gauge Fields in (A)dS d , Nucl. Phys. B 862 (2012) 341 [arXiv:1108.5921] [INSPIRE].
E. Joung and M. Taronna, Cubic interactions of massless higher spins in (A)dS: metric-like approach, Nucl. Phys. B 861 (2012) 145 [arXiv:1110.5918] [INSPIRE].
X. Bekaert, E. Joung and J. Mourad, On higher spin interactions with matter, JHEP 05 (2009) 126 [arXiv:0903.3338] [INSPIRE].
B. de Wit and D.Z. Freedman, Systematics of Higher Spin Gauge Fields, Phys. Rev. D 21 (1980) 358 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1112.5620
Unité Mixte de Recherche 7164 du CNRS
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Joung, E., Mourad, J. Boundary action of free AdS higher-spin gauge fields and the holographic correspondence. J. High Energ. Phys. 2012, 161 (2012). https://doi.org/10.1007/JHEP06(2012)161
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2012)161