Abstract
Many black hole solutions of General Relativity are known to be linearly exact. This opens a way to study them in gauge theories that apart from gravity contain fields of higher spin s > 2. Starting with a black brane in AdS4 we find its free field higher- spin generalization that respects static and planar symmetry for all bosonic gauge fields s ≥ 0. The solution is found for both the higher-spin curvatures and potentials in the form suitable for further non-linear analysis and satisfies the multi copy relation.
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 [Adv. Theor. Math. Phys. 2 (1998) 231] [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].
I.R. Klebanov and A.A. Tseytlin, Entropy of near extremal black p-branes, Nucl. Phys. B 475 (1996) 164 [hep-th/9604089] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [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. 660 (2003) 403] [hep-th/0205131] [INSPIRE].
R.G. Leigh and A.C. Petkou, Holography of the N = 1 higher spin theory on AdS4, JHEP 06 (2003) 011 [hep-th/0304217] [INSPIRE].
C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D 18 (1978) 3624 [INSPIRE].
A.K.H. Bengtsson, I. Bengtsson and L. Brink, Cubic Interaction Terms for Arbitrary Spin, Nucl. Phys. B 227 (1983) 31 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, On the Gravitational Interaction of Massless Higher Spin Fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].
R.R. Metsaev, Generating function for cubic interaction vertices of higher spin fields in any dimension, Mod. Phys. Lett. A 8 (1993) 2413 [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].
D. Sorokin, Introduction to the classical theory of higher spins, AIP Conf. Proc. 767 (2005) 172 [hep-th/0405069] [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, in The Many Faces of the Superworld. Yuri Golfand Memorial Volume, World Scientific (2000), pp. 533–610 [hep-th/9910096] [INSPIRE].
X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, in proceedings of the 1st Solvay Workshop on Higher Spin Gauge Theories, Brussels, Belgium, 12–14 May 2004, hep-th/0503128 [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Elements of Vasiliev theory, arXiv:1401.2975 [INSPIRE].
N. Boulanger and P. Sundell, An action principle for Vasiliev’s four-dimensional higher-spin gravity, J. Phys. A 44 (2011) 495402 [arXiv:1102.2219] [INSPIRE].
C. Sleight and M. Taronna, Higher Spin Interactions from Conformal Field Theory: The Complete Cubic Couplings, Phys. Rev. Lett. 116 (2016) 181602 [arXiv:1603.00022] [INSPIRE].
M.A. Vasiliev, From Coxeter Higher-Spin Theories to Strings and Tensor Models, JHEP 08 (2018) 051 [arXiv:1804.06520] [INSPIRE].
N. Misuna, On unfolded off-shell formulation for higher-spin theory, Phys. Lett. B 798 (2019) 134956 [arXiv:1905.06925] [INSPIRE].
S. Giombi and X. Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].
J.M. Maldacena and A. Zhiboedov, Constraining Conformal Field Theories with A Higher Spin Symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, d = 3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [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].
J.M. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].
O. Aharony, S. Giombi, G. Gur-Ari, J.M. Maldacena and R. Yacoby, The Thermal Free Energy in Large N Chern-Simons-Matter Theories, JHEP 03 (2013) 121 [arXiv:1211.4843] [INSPIRE].
S. Giombi and I.R. Klebanov, One Loop Tests of Higher Spin AdS/CFT, JHEP 12 (2013) 068 [arXiv:1308.2337] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT, JHEP 11 (2014) 114 [arXiv:1410.3273] [INSPIRE].
M.A. Vasiliev, Holography, Unfolding and Higher-Spin Theory, J. Phys. A 46 (2013) 214013 [arXiv:1203.5554] [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].
O.A. Gelfond and M.A. Vasiliev, Operator algebra of free conformal currents via twistors, Nucl. Phys. B 876 (2013) 871 [arXiv:1301.3123] [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∞ as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, An AdS3 Dual for Minimal Model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].
M. Gutperle and P. Kraus, Higher Spin Black Holes, JHEP 05 (2011) 022 [arXiv:1103.4304] [INSPIRE].
S.H. Shenker and X. Yin, Vector Models in the Singlet Sector at Finite Temperature, arXiv:1109.3519 [INSPIRE].
V.E. Didenko and A.V. Korybut, Planar solutions of higher-spin theory II: nonlinear corrections, in preparation.
X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory, JHEP 11 (2015) 149 [arXiv:1508.04292] [INSPIRE].
C. Sleight and M. Taronna, Higher-Spin Gauge Theories and Bulk Locality, Phys. Rev. Lett. 121 (2018) 171604 [arXiv:1704.07859] [INSPIRE].
A.C. Petkou, Evaluating the AdS dual of the critical O(N) vector model, JHEP 03 (2003) 049 [hep-th/0302063] [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].
M.A. Vasiliev, Dynamics of Massless Higher Spins in the Second Order in Curvatures, Phys. Lett. B 238 (1990) 305 [INSPIRE].
O.A. Gelfond and M.A. Vasiliev, Homotopy Operators and Locality Theorems in Higher-Spin Equations, Phys. Lett. B 786 (2018) 180 [arXiv:1805.11941] [INSPIRE].
M.A. Vasiliev, Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations, JHEP 10 (2017) 111 [arXiv:1605.02662] [INSPIRE].
V.E. Didenko, O.A. Gelfond, A.V. Korybut and M.A. Vasiliev, Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations, J. Phys. A 51 (2018) 465202 [arXiv:1807.00001] [INSPIRE].
V.E. Didenko, O.A. Gelfond, A.V. Korybut and M.A. Vasiliev, Limiting Shifted Homotopy in Higher-Spin Theory and Spin-Locality, JHEP 12 (2019) 086 [arXiv:1909.04876] [INSPIRE].
O.A. Gelfond and M.A. Vasiliev, Spin-Locality of Higher-Spin Theories and Star-Product Functional Classes, JHEP 03 (2020) 002 [arXiv:1910.00487] [INSPIRE].
V.E. Didenko, O.A. Gelfond, A.V. Korybut and M.A. Vasiliev, Spin-locality of η2 and \( \overline{\eta} \)2 quartic higher-spin vertices, JHEP 12 (2020) 184 [arXiv:2009.02811] [INSPIRE].
O.A. Gelfond and A.V. Korybut, Manifest form of the spin-local higher-spin vertex \( {\mathrm{Y}}_{\omega CCC}^{\eta \eta} \), Eur. Phys. J. C 81 (2021) 605 [arXiv:2101.01683] [INSPIRE].
E. Sezgin and P. Sundell, An Exact solution of 4D higher-spin gauge theory, Nucl. Phys. B 762 (2007) 1 [hep-th/0508158] [INSPIRE].
C. Iazeolla, E. Sezgin and P. Sundell, Real forms of complex higher spin field equations and new exact solutions, Nucl. Phys. B 791 (2008) 231 [arXiv:0706.2983] [INSPIRE].
V.E. Didenko and M.A. Vasiliev, Static BPS black hole in 4d higher-spin gauge theory, Phys. Lett. B 682 (2009) 305 [Erratum ibid. 722 (2013) 389] [arXiv:0906.3898] [INSPIRE].
C. Iazeolla and P. Sundell, Families of exact solutions to Vasiliev’s 4D equations with spherical, cylindrical and biaxial symmetry, JHEP 12 (2011) 084 [arXiv:1107.1217] [INSPIRE].
P. Sundell and Y. Yin, New classes of bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity, JHEP 01 (2017) 043 [arXiv:1610.03449] [INSPIRE].
C. Iazeolla and P. Sundell, 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations, JHEP 10 (2017) 130 [arXiv:1705.06713] [INSPIRE].
C. Iazeolla and J. Raeymaekers, On big crunch solutions in Prokushkin-Vasiliev theory, JHEP 01 (2016) 177 [arXiv:1510.08835] [INSPIRE].
C. Iazeolla, E. Sezgin and P. Sundell, On Exact Solutions and Perturbative Schemes in Higher Spin Theory, Universe 4 (2018) 5 [arXiv:1711.03550] [INSPIRE].
R. Aros, C. Iazeolla, J. Noreña, E. Sezgin, P. Sundell and Y. Yin, FRW and domain walls in higher spin gravity, JHEP 03 (2018) 153 [arXiv:1712.02401] [INSPIRE].
J. Bourdier and N. Drukker, On Classical Solutions of 4d Supersymmetric Higher Spin Theory, JHEP 04 (2015) 097 [arXiv:1411.7037] [INSPIRE].
A. David and Y. Neiman, Bulk interactions and boundary dual of higher-spin-charged particles, JHEP 03 (2021) 264 [arXiv:2009.02893] [INSPIRE].
V.E. Didenko, A.S. Matveev and M.A. Vasiliev, Unfolded Dynamics and Parameter Flow of Generic AdS4 Black Hole, arXiv:0901.2172 [INSPIRE].
V.E. Didenko, A.S. Matveev and M.A. Vasiliev, unpublished.
T. Adamo, Lectures on twistor theory, PoS Modave2017 (2018) 003 [arXiv:1712.02196] [INSPIRE].
C.D. White, Twistorial Foundation for the Classical Double Copy, Phys. Rev. Lett. 126 (2021) 061602 [arXiv:2012.02479] [INSPIRE].
M. Walker and R. Penrose, On quadratic first integrals of the geodesic equations for type {22} spacetimes, Commun. Math. Phys. 18 (1970) 265 [INSPIRE].
R.M. Floyd, The dynamics of Kerr fields, Ph.D. Thesis, London University, London U.K. (1974).
O.A. Gelfond and M.A. Vasiliev, Sp(8) invariant higher spin theory, twistors and geometric BRST formulation of unfolded field equations, JHEP 12 (2009) 021 [arXiv:0901.2176] [INSPIRE].
Y. Neiman, The holographic dual of the Penrose transform, JHEP 01 (2018) 100 [arXiv:1709.08050] [INSPIRE].
V.E. Didenko, N.G. Misuna and M.A. Vasiliev, Charges in nonlinear higher-spin theory, JHEP 03 (2017) 164 [arXiv:1512.07626] [INSPIRE].
K.I. Bolotin and M.A. Vasiliev, Star product and massless free field dynamics in AdS4, Phys. Lett. B 479 (2000) 421 [hep-th/0001031] [INSPIRE].
B. Nagaraj and D. Ponomarev, Spinor-helicity formalism for massless fields in AdS4. Part II. Potentials, JHEP 06 (2020) 068 [arXiv:1912.07494] [INSPIRE].
V.E. Didenko and M.A. Vasiliev, Test of the local form of higher-spin equations via AdS/CFT, Phys. Lett. B 775 (2017) 352 [arXiv:1705.03440] [INSPIRE].
A. David and Y. Neiman, Higher-spin symmetry vs. boundary locality, and a rehabilitation of dS/CFT, JHEP 10 (2020) 127 [arXiv:2006.15813] [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Towards higher-spin holography in ambient space of any dimension, J. Phys. A 46 (2013) 214010 [arXiv:1207.6786] [INSPIRE].
V. Didenko, On higher-spin black brane, in proceedings of the 2nd Solvay Workshop on “Higher Spin Gauge Theories”, Brussels, Belgium, 5–8 February 2013.
Y. Yasui and T. Houri, Hidden Symmetry and Exact Solutions in Einstein Gravity, Prog. Theor. Phys. Suppl. 189 (2011) 126 [arXiv:1104.0852] [INSPIRE].
V.E. Didenko, A.S. Matveev and M.A. Vasiliev, Unfolded Description of AdS4 Kerr Black Hole, Phys. Lett. B 665 (2008) 284 [arXiv:0801.2213] [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].
J. Engquist and P. Sundell, Brane partons and singleton strings, Nucl. Phys. B 752 (2006) 206 [hep-th/0508124] [INSPIRE].
C. Iazeolla and P. Sundell, A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations, JHEP 10 (2008) 022 [arXiv:0806.1942] [INSPIRE].
D. De Filippi, C. Iazeolla and P. Sundell, Fronsdal fields from gauge functions in Vasiliev’s higher spin gravity, JHEP 10 (2019) 215 [arXiv:1905.06325] [INSPIRE].
R. Aros, C. Iazeolla, P. Sundell and Y. Yin, Higher spin fluctuations on spinless 4D BTZ black hole, JHEP 08 (2019) 171 [arXiv:1903.01399] [INSPIRE].
C. Iazeolla, On boundary conditions and spacetime/fibre duality in Vasiliev’s higher-spin gravity, PoS CORFU2019 (2020) 181 [arXiv:2004.14903] [INSPIRE].
R. Monteiro, D. O’Connell and C.D. White, Black holes and the double copy, JHEP 12 (2014) 056 [arXiv:1410.0239] [INSPIRE].
E. Sezgin, E.D. Skvortsov and Y. Zhu, Chern-Simons Matter Theories and Higher Spin Gravity, JHEP 07 (2017) 133 [arXiv:1705.03197] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2105.09021
Rights and permissions
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.
About this article
Cite this article
Didenko, V.E., Korybut, A.V. Planar solutions of higher-spin theory. Part I. Free field level. J. High Energ. Phys. 2021, 144 (2021). https://doi.org/10.1007/JHEP08(2021)144
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2021)144