Abstract
We study the higher-spin extension of self-dual General Relativity (GR) with cosmological constant, proposed by Krasnov, Skvortsov and Tran. We show that this theory is actually a gauge-fixing of a 6d diffeomorphism-invariant Abelian theory, living on (4d spacetime)×(2d spinor space) modulo a finite group. On the other hand, we point out that the theory respects the 4d geometry of a self-dual GR solution, with no backreaction from the higher-spin fields. We also present a lightcone ansatz that reduces the covariant fields to one scalar field for each helicity. The field equations governing these scalars have only cubic vertices. We compare our lightcone ansatz to Metsaev’s lightcone formalism. We conclude with a new perspective on the lightcone formalism in (A)dS spacetime: not merely a complication of its Minkowski-space cousin, it has a built-in Lorentz covariance, and is closely related to Vasiliev’s concept of unfolding.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
M.A. Vasiliev, Higher spin gauge theories: star product and AdS space, hep-th/9910096 [https://doi.org/10.1142/9789812793850_0030] [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 [hep-th/0205131] [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, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [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. Lysov and Y. Neiman, Higher-spin gravity’s “string”: new gauge and proof of holographic duality for the linearized Didenko-Vasiliev solution, JHEP 10 (2022) 054 [arXiv:2207.07507] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, Class. Quant. Grav. 34 (2017) 015009 [arXiv:1108.5735] [INSPIRE].
A. Fotopoulos and M. Tsulaia, On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations, JHEP 11 (2010) 086 [arXiv:1009.0727] [INSPIRE].
M. Taronna, Higher-Spin Interactions: four-point functions and beyond, JHEP 04 (2012) 029 [arXiv:1107.5843] [INSPIRE].
M.A. Vasiliev, Star-Product Functions in Higher-Spin Theory and Locality, JHEP 06 (2015) 031 [arXiv:1502.02271] [INSPIRE].
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].
E.D. Skvortsov and M. Taronna, On Locality, Holography and Unfolding, JHEP 11 (2015) 044 [arXiv:1508.04764] [INSPIRE].
C. Sleight and M. Taronna, Higher-Spin Gauge Theories and Bulk Locality, Phys. Rev. Lett. 121 (2018) 171604 [arXiv:1704.07859] [INSPIRE].
D. Ponomarev, A Note on (Non)-Locality in Holographic Higher Spin Theories, Universe 4 (2018) 2 [arXiv:1710.00403] [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].
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].
M.A. Vasiliev, Projectively-compact spinor vertices and space-time spin-locality in higher-spin theory, Phys. Lett. B 834 (2022) 137401 [arXiv:2208.02004] [INSPIRE].
Y. Neiman, Quartic locality of higher-spin gravity in de Sitter and Euclidean anti-de Sitter space, Phys. Lett. B 843 (2023) 138048 [arXiv:2302.00852] [INSPIRE].
K. Krasnov, Self-Dual Gravity, Class. Quant. Grav. 34 (2017) 095001 [arXiv:1610.01457] [INSPIRE].
W.A. Bardeen, Selfdual Yang-Mills theory, integrability and multiparton amplitudes, Prog. Theor. Phys. Suppl. 123 (1996) 1 [INSPIRE].
A.A. Rosly and K.G. Selivanov, On amplitudes in selfdual sector of Yang-Mills theory, Phys. Lett. B 399 (1997) 135 [hep-th/9611101] [INSPIRE].
L.J. Mason and D. Skinner, Gravity, Twistors and the MHV Formalism, Commun. Math. Phys. 294 (2010) 827 [arXiv:0808.3907] [INSPIRE].
A. David, N. Fischer and Y. Neiman, Spinor-helicity variables for cosmological horizons in de Sitter space, Phys. Rev. D 100 (2019) 045005 [arXiv:1906.01058] [INSPIRE].
E. Albrychiewicz and Y. Neiman, Scattering in the static patch of de Sitter space, Phys. Rev. D 103 (2021) 065014 [arXiv:2012.13584] [INSPIRE].
E. Albrychiewicz, Y. Neiman and M. Tsulaia, MHV amplitudes and BCFW recursion for Yang-Mills theory in the de Sitter static patch, JHEP 09 (2021) 176 [arXiv:2105.07572] [INSPIRE].
Y. Neiman, Self-dual gravity in de Sitter space: light-cone ansatz and static-patch scattering, Phys. Rev. D 109 (2024) 024039 [arXiv:2303.17866] [INSPIRE].
D. Ponomarev and E.D. Skvortsov, Light-Front Higher-Spin Theories in Flat Space, J. Phys. A 50 (2017) 095401 [arXiv:1609.04655] [INSPIRE].
E.D. Skvortsov, T. Tran and M. Tsulaia, Quantum Chiral Higher Spin Gravity, Phys. Rev. Lett. 121 (2018) 031601 [arXiv:1805.00048] [INSPIRE].
E. Skvortsov, T. Tran and M. Tsulaia, More on Quantum Chiral Higher Spin Gravity, Phys. Rev. D 101 (2020) 106001 [arXiv:2002.08487] [INSPIRE].
E. Skvortsov, Light-Front Bootstrap for Chern-Simons Matter Theories, JHEP 06 (2019) 058 [arXiv:1811.12333] [INSPIRE].
R.R. Metsaev, Light-cone gauge cubic interaction vertices for massless fields in AdS(4), Nucl. Phys. B 936 (2018) 320 [arXiv:1807.07542] [INSPIRE].
E. Skvortsov and R. Van Dongen, Minimal models of field theories: chiral higher spin gravity, Phys. Rev. D 106 (2022) 045006 [arXiv:2204.10285] [INSPIRE].
A. Sharapov et al., Minimal model of Chiral Higher Spin Gravity, JHEP 09 (2022) 134 [Erratum ibid. 02 (2023) 183] [arXiv:2205.07794] [INSPIRE].
A. Sharapov and E. Skvortsov, Chiral higher spin gravity in (A)dS4 and secrets of Chern-Simons matter theories, Nucl. Phys. B 985 (2022) 115982 [arXiv:2205.15293] [INSPIRE].
V.E. Didenko, On holomorphic sector of higher-spin theory, JHEP 10 (2022) 191 [arXiv:2209.01966] [INSPIRE].
D. Ponomarev, Chiral Higher Spin Theories and Self-Duality, JHEP 12 (2017) 141 [arXiv:1710.00270] [INSPIRE].
K. Krasnov, E. Skvortsov and T. Tran, Actions for self-dual Higher Spin Gravities, JHEP 08 (2021) 076 [arXiv:2105.12782] [INSPIRE].
K. Krasnov, Gravity as a diffeomorphism invariant gauge theory, Phys. Rev. D 84 (2011) 024034 [arXiv:1101.4788] [INSPIRE].
K. Krasnov, Pure Connection Action Principle for General Relativity, Phys. Rev. Lett. 106 (2011) 251103 [arXiv:1103.4498] [INSPIRE].
R. Capovilla, T. Jacobson and J. Dell, General Relativity Without the Metric, Phys. Rev. Lett. 63 (1989) 2325 [INSPIRE].
R. Capovilla, T. Jacobson and J. Dell, Gravitational instantons as SU(2) gauge fields, Class. Quant. Grav. 7 (1990) L1 [INSPIRE].
Y. Herfray, Pure Connection Formulation, Twistors and the Chase for a Twistor Action for General Relativity, J. Math. Phys. 58 (2017) 112505 [arXiv:1610.02343] [INSPIRE].
J.F. Plebanski, Some solutions of complex Einstein equations, J. Math. Phys. 16 (1975) 2395 [INSPIRE].
W. Siegel, Selfdual N = 8 supergravity as closed N = 2 (N = 4) strings, Phys. Rev. D 47 (1993) 2504 [hep-th/9207043] [INSPIRE].
R.R. Metsaev, Cubic interaction vertices of massive and massless higher spin fields, Nucl. Phys. B 759 (2006) 147 [hep-th/0512342] [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].
Y. Herfray, K. Krasnov and E. Skvortsov, Higher-spin self-dual Yang-Mills and gravity from the twistor space, JHEP 01 (2023) 158 [arXiv:2210.06209] [INSPIRE].
R. Penrose, Nonlinear Gravitons and Curved Twistor Theory, Gen. Rel. Grav. 7 (1976) 31 [INSPIRE].
R.S. Ward, Self-dual space-times with cosmological constant, Commun. Math. Phys. 78 (1980) 1 [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].
R.R. Metsaev, Massive totally symmetric fields in AdS(d), Phys. Lett. B 590 (2004) 95 [hep-th/0312297] [INSPIRE].
R. Penrose, Null hypersurface initial data for classical fields of arbitrary spin and for general relativity, Gen. Rel. Grav. 12 (1980) 225 [INSPIRE].
A. Lipstein and S. Nagy, Self-Dual Gravity and Color-Kinematics Duality in AdS4, Phys. Rev. Lett. 131 (2023) 081501 [arXiv:2304.07141] [INSPIRE].
Acknowledgments
I am grateful to Kirill Krasnov, Evgeny Skvortsov, Tung Tran, Julian Lang, Slava Lysov and Mirian Tsulaia for discussions, and to Dmitry Ponomarev for an email exchange. This work was supported by the Quantum Gravity Unit of the Okinawa Institute of Science and Technology Graduate University (OIST). The conceptual picture was finalized at the 5th Mons Workshop on Higher-Spin Gauge Theories.
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: 2404.18589
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
Neiman, Y. Higher-spin self-dual General Relativity: 6d and 4d pictures, covariant vs. lightcone. J. High Energ. Phys. 2024, 178 (2024). https://doi.org/10.1007/JHEP07(2024)178
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2024)178