Abstract
We study the functional class and locality problems in the context of higher-spin theories and Vasiliev’s equations. A locality criterion that is sufficient to make higher-spin theories well-defined as field theories on Anti-de-Sitter space is proposed. This criterion identifies admissible pseudo-local field redefinitions which preserve AdS/CFT correlation functions as we check in the 3d example. Implications of this analysis for known higher-spin theories are discussed. We also check that the cubic coupling coefficients previously fixed in 3d at the action level give the correct CFT correlation functions upon computing the corresponding Witten diagrams.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [INSPIRE].
X. Bekaert, N. Boulanger and P. Sundell, How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples, Rev. Mod. Phys. 84 (2012) 987 [arXiv:1007.0435] [INSPIRE].
M. Taronna, Higher-Spin Interactions: three-point functions and beyond, arXiv:1209.5755.
S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
A. Sagnotti, Notes on Strings and Higher Spins, J. Phys. A 46 (2013) 214006 [arXiv:1112.4285] [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Elements of Vasiliev theory, arXiv:1401.2975 [INSPIRE].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3+1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
S.F. Prokushkin and M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [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].
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].
M.R. Gaberdiel and R. Gopakumar, An AdS 3 Dual for Minimal Model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].
M. Bianchi, J.F. Morales and H. Samtleben, On stringy AdS 5 × S 5 and higher spin holography, JHEP 07 (2003) 062 [hep-th/0305052] [INSPIRE].
J. Engquist and P. Sundell, Brane partons and singleton strings, Nucl. Phys. B 752 (2006) 206 [hep-th/0508124] [INSPIRE].
M. Taronna, Higher Spins and String Interactions, arXiv:1005.3061.
A. Sagnotti and M. Taronna, String Lessons for Higher-Spin Interactions, Nucl. Phys. B 842 (2011) 299 [arXiv:1006.5242] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Higher Spins & Strings, JHEP 11 (2014) 044 [arXiv:1406.6103] [INSPIRE].
S. Giombi, S. Minwalla, S. Prakash, S.P. Trivedi, S.R. Wadia and X. Yin, Chern-Simons Theory with Vector Fermion Matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ Triality: from Higher Spin Fields to Strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [INSPIRE].
E. Sezgin and P. Sundell, Analysis of higher spin field equations in four-dimensions, JHEP 07 (2002) 055 [hep-th/0205132] [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].
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].
C.-M. Chang and X. Yin, Higher Spin Gravity with Matter in AdS 3 and Its CFT Dual, JHEP 10 (2012) 024 [arXiv:1106.2580] [INSPIRE].
M. Ammon, P. Kraus and E. Perlmutter, Scalar fields and three-point functions in D = 3 higher spin gravity, JHEP 07 (2012) 113 [arXiv:1111.3926] [INSPIRE].
P. Kessel, G. Lucena Gomez, E.D. Skvortsov and M. Taronna, Higher Spins and Matter Interacting in Dimension Three, arXiv:1505.05887 [INSPIRE].
N. Boulanger, P. Kessel, E.D. Skvortsov and M. Taronna, Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal, arXiv:1508.04139 [INSPIRE].
M.A. Vasiliev, Equations of Motion of Interacting Massless Fields of All Spins as a Free Differential Algebra, Phys. Lett. B 209 (1988) 491 [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, hep-th/9910096 [INSPIRE].
M.A. Vasiliev, Star-Product Functions in Higher-Spin Theory and Locality, JHEP 06 (2015) 031 [arXiv:1502.02271] [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, Higher spin symmetries, star product and relativistic equations in AdS space, hep-th/0002183 [INSPIRE].
M.A. Vasiliev, Higher spin superalgebras in any dimension and their representations, JHEP 12 (2004) 046 [hep-th/0404124] [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].
R.R. Metsaev, Cubic interaction vertices of massive and massless higher spin fields, Nucl. Phys. B 759 (2006) 147 [hep-th/0512342] [INSPIRE].
S.F. Prokushkin and M.A. Vasiliev, Cohomology of arbitrary spin currents in AdS 3, Theor. Math. Phys. 123 (2000) 415 [hep-th/9907020] [INSPIRE].
M. Taronna, Higher-Spin Interactions: four-point functions and beyond, JHEP 04 (2012) 029 [arXiv:1107.5843] [INSPIRE].
G. Barnich and M. Henneaux, Consistent couplings between fields with a gauge freedom and deformations of the master equation, Phys. Lett. B 311 (1993) 123 [hep-th/9304057] [INSPIRE].
C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D 18 (1978) 3624 [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].
E. Joung, L. Lopez and M. Taronna, Solving the Noether procedure for cubic interactions of higher spins in (A)dS, J. Phys. A 46 (2013) 214020 [arXiv:1207.5520] [INSPIRE].
N. Moeller and B. Zwiebach, Dynamics with infinitely many time derivatives and rolling tachyons, JHEP 10 (2002) 034 [hep-th/0207107] [INSPIRE].
T. Biswas, A. Mazumdar and W. Siegel, Bouncing universes in string-inspired gravity, JCAP 03 (2006) 009 [hep-th/0508194] [INSPIRE].
M.A. Vasiliev, Invariant Functionals in Higher-Spin Theory, arXiv:1504.07289 [INSPIRE].
E. Joung and M. Taronna, Cubic-interaction-induced deformations of higher-spin symmetries, JHEP 03 (2014) 103 [arXiv:1311.0242] [INSPIRE].
O.A. Gelfond and M.A. Vasiliev, Unfolded Equations for Current Interactions of 4d Massless Fields as a Free System in Mixed Dimensions, J. Exp. Theor. Phys. 120 (2015) 484 [arXiv:1012.3143] [INSPIRE].
M.A. Vasiliev, Consistent Equations for Interacting Massless Fields of All Spins in the First Order in Curvatures, Annals Phys. 190 (1989) 59 [INSPIRE].
M.A. Vasiliev, Unfolded representation for relativistic equations in (2+1) anti-de Sitter space, Class. Quant. Grav. 11 (1994) 649 [INSPIRE].
O.A. Gelfond, E.D. Skvortsov and M.A. Vasiliev, Higher spin conformal currents in Minkowski space, Theor. Math. Phys. 154 (2008) 294 [hep-th/0601106] [INSPIRE].
X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory, arXiv:1508.04292 [INSPIRE].
C. Sleight and M. Taronna, Scalar Back-reaction from Higher-Spin Algebras: Unfolding and the Cubic Action, to appear (2015).
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].
C.-M. Chang and X. Yin, Correlators in W N Minimal Model Revisited, JHEP 10 (2012) 050 [arXiv:1112.5459] [INSPIRE].
K.B. Alkalaev and V.A. Belavin, Classical conformal blocks via AdS/CFT correspondence, JHEP 08 (2015) 049 [arXiv:1504.05943] [INSPIRE].
E. Hijano, P. Kraus and R. Snively, Worldline approach to semi-classical conformal blocks, JHEP 07 (2015) 131 [arXiv:1501.02260] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Universality of Long-Distance AdS Physics from the CFT Bootstrap, JHEP 08 (2014) 145 [arXiv:1403.6829] [INSPIRE].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
M. Henneaux and S.-J. Rey, Nonlinear W ∞ as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [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].
N. Boulanger, S. Leclercq and P. Sundell, On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory, JHEP 08 (2008) 056 [arXiv:0805.2764] [INSPIRE].
N. Colombo and P. Sundell, Twistor space observables and quasi-amplitudes in 4D higher spin gravity, JHEP 11 (2011) 042 [arXiv:1012.0813] [INSPIRE].
N. Colombo and P. Sundell, Higher Spin Gravity Amplitudes From Zero-form Charges, arXiv:1208.3880 [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory, JHEP 04 (2013) 158 [arXiv:1210.7963] [INSPIRE].
V.E. Didenko, J. Mei and E.D. Skvortsov, Exact higher-spin symmetry in CFT: free fermion correlators from Vasiliev Theory, Phys. Rev. D 88 (2013) 046011 [arXiv:1301.4166] [INSPIRE].
X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange, JHEP 03 (2015) 170 [arXiv:1412.0016] [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: 1508.04764
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
Skvortsov, E., Taronna, M. On locality, holography and unfolding. J. High Energ. Phys. 2015, 44 (2015). https://doi.org/10.1007/JHEP11(2015)044
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)044