Abstract
We consider type-A higher-spin gravity in 4 dimensions, holographically dual to a free O(N) vector model. In this theory, the cubic correlators of higher-spin boundary currents are reproduced in the bulk by the Sleight-Taronna cubic vertex. We extend these cubic correlators from local boundary currents to bilocal boundary operators, which contain the tower of local currents in their Taylor expansion. In the bulk, these boundary bilocals are represented by linearized Didenko-Vasiliev (DV) “black holes”. We argue that the cubic correlators are still described by local bulk structures, which include a new vertex coupling two higher-spin fields to the “worldline” of a DV solution. As an illustration of the general argument, we analyze numerically the correlator of two local scalars and one bilocal. We also prove a gauge-invariance property of the Sleight-Taronna vertex outside its original range of applicability: in the absence of sources, it is invariant not just within transverse-traceless gauge, but rather in general traceless gauge, which in particular includes the DV solution away from its “worldline”.
Article PDF
Similar content being viewed by others
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 [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].
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].
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].
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].
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].
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. 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].
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, A.S. Matveev and M.A. Vasiliev, Unfolded Description of AdS4 Kerr Black Hole, Phys. Lett. B 665 (2008) 284 [arXiv:0801.2213] [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].
J.H. Schwarz, Lectures on superstring and M-theory dualities: Given at ICTP Spring School and at TASI Summer School, Nucl. Phys. B Proc. Suppl. 55 (1997) 1 [hep-th/9607201] [INSPIRE].
R. Blumenhagen, D. Lüst and S. Theisen, Basic concepts of string theory, Theoretical and Mathematical Physics, Springer, Heidelberg, Germany (2013), https://doi.org/10.1007/978-3-642-29497-6 [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [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].
S.R. Das and A. Jevicki, Large N collective fields and holography, Phys. Rev. D 68 (2003) 044011 [hep-th/0304093] [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].
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].
Y. Neiman, New diagrammatic framework for higher-spin gravity, arXiv:2209.02185 [INSPIRE].
C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D 18 (1978) 3624 [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].
T. Biswas and W. Siegel, Radial dimensional reduction: Anti-de Sitter theories from flat, JHEP 07 (2002) 005 [hep-th/0203115] [INSPIRE].
E.D. Skvortsov and M.A. Vasiliev, Transverse Invariant Higher Spin Fields, Phys. Lett. B 664 (2008) 301 [hep-th/0701278] [INSPIRE].
A. Campoleoni and D. Francia, Maxwell-like Lagrangians for higher spins, JHEP 03 (2013) 168 [arXiv:1206.5877] [INSPIRE].
N.S. Craigie, V.K. Dobrev and I.T. Todorov, Conformally Covariant Composite Operators in Quantum Chromodynamics, Annals Phys. 159 (1985) 411 [INSPIRE].
D. Anselmi, Higher spin current multiplets in operator product expansions, Class. Quant. Grav. 17 (2000) 1383 [hep-th/9906167] [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].
A. Mikhailov, Notes on higher spin symmetries, hep-th/0201019 [INSPIRE].
Y. Neiman, The holographic dual of the Penrose transform, JHEP 01 (2018) 100 [arXiv:1709.08050] [INSPIRE].
E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks, JHEP 01 (2016) 146 [arXiv:1508.00501] [INSPIRE].
E. Dyer, D.Z. Freedman and J. Sully, Spinning Geodesic Witten Diagrams, JHEP 11 (2017) 060 [arXiv:1702.06139] [INSPIRE].
I.L. Buchbinder, A. Fotopoulos, A.C. Petkou and M. Tsulaia, Constructing the cubic interaction vertex of higher spin gauge fields, Phys. Rev. D 74 (2006) 105018 [hep-th/0609082] [INSPIRE].
Wikipedia, Spherical harmonics — Higher dimensions, https://en.wikipedia.org/wiki/Spherical_harmonics#Higher_dimensions.
Digital Library of Mathematical Functions, Special Values, https://dlmf.nist.gov/14.5.
D. Francia, G.L. Monaco and K. Mkrtchyan, Cubic interactions of Maxwell-like higher spins, JHEP 04 (2017) 068 [arXiv:1611.00292] [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: 2209.00854
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
Lysov, V., Neiman, Y. Bulk locality and gauge invariance for boundary-bilocal cubic correlators in higher-spin gravity. J. High Energ. Phys. 2022, 142 (2022). https://doi.org/10.1007/JHEP12(2022)142
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2022)142