Abstract
We construct a double field theory coupled to the fields present in Vasiliev’s equations. Employing the “semi-covariant” differential geometry, we spell a functional in which each term is completely covariant with respect to O(4, 4) T-duality, doubled diffeomorphisms, Spin(1, 3) local Lorentz symmetry and, separately, HS(4) higher spin gauge symmetry. We identify a minimal set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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].
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].
X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Elements of Vasiliev theory, arXiv:1401.2975 [INSPIRE].
M.A. Vasiliev, Higher-Spin Theory and Space-Time Metamorphoses, Lect. Notes Phys. 892 (2015) 227 [arXiv:1404.1948] [INSPIRE].
M.A. Vasiliev, Symmetries and Invariants in Higher-Spin Theory, arXiv:1603.01888 [INSPIRE].
E.S. Fradkin, The problem of unification of all interactions and self-consistency, preprint Lebedev 90-0193, talk given at Dirac Medal for 1988, Trieste, Italy, April 1989.
D.J. Gross and P.F. Mende, The High-Energy Behavior of String Scattering Amplitudes, Phys. Lett. B 197 (1987) 129 [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].
R. Rahman, Higher Spin Theory — Part I, PoS(Modave VIII)004 [arXiv:1307.3199] [INSPIRE].
M. Bianchi and V. Didenko, Massive higher spin multiplets and holography, hep-th/0502220 [INSPIRE].
X. Bekaert, E. Joung and J. Mourad, Comments on higher-spin holography, Fortsch. Phys. 60 (2012) 882 [arXiv:1202.0543] [INSPIRE].
S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
A. Sagnotti, Notes on Strings and Higher Spins, J. Phys. A 46 (2013) 214006 [arXiv:1112.4285] [INSPIRE].
W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
C. Hull and B. Zwiebach, The gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].
G. Aldazabal, D. Marques and C. Núñez, Double Field Theory: A Pedagogical Review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].
D.S. Berman and D.C. Thompson, Duality Symmetric String and M-theory, Phys. Rept. 566 (2014) 1 [arXiv:1306.2643] [INSPIRE].
O. Hohm, D. Lüst and B. Zwiebach, The Spacetime of Double Field Theory: Review, Remarks and Outlook, Fortsch. Phys. 61 (2013) 926 [arXiv:1309.2977] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Differential geometry with a projection: Application to double field theory, JHEP 04 (2011) 014 [arXiv:1011.1324] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Stringy differential geometry, beyond Riemann, Phys. Rev. D 84 (2011) 044022 [arXiv:1105.6294] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Double field formulation of Yang-Mills theory, Phys. Lett. B 701 (2011) 260 [arXiv:1102.0419] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Incorporation of fermions into double field theory, JHEP 11 (2011) 025 [arXiv:1109.2035] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Ramond-Ramond Cohomology and O(D, D) T-duality, JHEP 09 (2012) 079 [arXiv:1206.3478] [INSPIRE].
N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. 54 (2003) 281 [math/0209099] [INSPIRE].
N. Hitchin, Lectures on generalized geometry, arXiv:1008.0973 [INSPIRE].
M. Gualtieri, Generalized complex geometry, math/0401221 [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity, Phys. Rev. D 85 (2012) 081501 [Erratum ibid. D 86 (2012) 089903] [arXiv:1112.0069] [INSPIRE].
I. Jeon, K. Lee, J.-H. Park and Y. Suh, Stringy Unification of Type IIA and IIB Supergravities under N = 2 D = 10 Supersymmetric Double Field Theory, Phys. Lett. B 723 (2013) 245 [arXiv:1210.5078] [INSPIRE].
K.-S. Choi and J.-H. Park, Standard Model as a Double Field Theory, Phys. Rev. Lett. 115 (2015) 171603 [arXiv:1506.05277] [INSPIRE].
S.M. Ko, C. Melby-Thompson, R. Meyer and J.-H. Park, Dynamics of Perturbations in Double Field Theory & Non-Relativistic String Theory, JHEP 12 (2015) 144 [arXiv:1508.01121] [INSPIRE].
C.D.A. Blair, Conserved Currents of Double Field Theory, JHEP 04 (2016) 180 [arXiv:1507.07541] [INSPIRE].
J.-H. Park, S.-J. Rey, W. Rim and Y. Sakatani, O(D, D) covariant Noether currents and global charges in double field theory, JHEP 11 (2015) 131 [arXiv:1507.07545] [INSPIRE].
O. Hohm and S.K. Kwak, Frame-like Geometry of Double Field Theory, J. Phys. A 44 (2011) 085404 [arXiv:1011.4101] [INSPIRE].
O. Hohm, S.K. Kwak and B. Zwiebach, Unification of Type II Strings and T-duality, Phys. Rev. Lett. 107 (2011) 171603 [arXiv:1106.5452] [INSPIRE].
D.S. Berman, C.D.A. Blair, E. Malek and M.J. Perry, The O(D, D) geometry of string theory, Int. J. Mod. Phys. A 29 (2014) 1450080 [arXiv:1303.6727] [INSPIRE].
O. Hohm and D. Marques, Perturbative Double Field Theory on General Backgrounds, Phys. Rev. D 93 (2016) 025032 [arXiv:1512.02658] [INSPIRE].
K.B. Alkalaev, M. Grigoriev and E.D. Skvortsov, Uniformizing higher-spin equations, J. Phys. A 48 (2015) 015401 [arXiv:1409.6507] [INSPIRE].
C. Arias et al., Action principles for higher and fractional spin gravities, arXiv:1603.04454 [INSPIRE].
M.A. Vasiliev, Invariant Functionals in Higher-Spin Theory, arXiv:1504.07289 [INSPIRE].
J.-H. Park, Comments on double field theory and diffeomorphisms, JHEP 06 (2013) 098 [arXiv:1304.5946] [INSPIRE].
K. Lee and J.-H. Park, Covariant action for a string in “doubled yet gauged” spacetime, Nucl. Phys. B 880 (2014) 134 [arXiv:1307.8377] [INSPIRE].
E. Malek, Timelike U-dualities in Generalised Geometry, JHEP 11 (2013) 185 [arXiv:1301.0543] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and D. Waldram, T-duality, Generalized Geometry and Non-Geometric Backgrounds, JHEP 04 (2009) 075 [arXiv:0807.4527] [INSPIRE].
W. Cho, J.J. Fernández-Melgarejo, I. Jeon and J.-H. Park, Supersymmetric gauged double field theory: systematic derivation by virtue of twist, JHEP 08 (2015) 084 [arXiv:1505.01301] [INSPIRE].
D.S. Berman, M. Cederwall and M.J. Perry, Global aspects of double geometry, JHEP 09 (2014) 066 [arXiv:1401.1311] [INSPIRE].
C.M. Hull, Finite Gauge Transformations and Geometry in Double Field Theory, JHEP 04 (2015) 109 [arXiv:1406.7794] [INSPIRE].
U. Naseer, A note on large gauge transformations in double field theory, JHEP 06 (2015) 002 [arXiv:1504.05913] [INSPIRE].
S.-J. Rey and Y. Sakatani, Finite Transformations in Doubled and Exceptional Space, arXiv:1510.06735 [INSPIRE].
T. Kugo and P.K. Townsend, Supersymmetry and the Division Algebras, Nucl. Phys. B 221 (1983) 357 [INSPIRE].
M. Cederwall, Twistors and supertwistors for exceptional field theory, JHEP 12 (2015) 123 [arXiv:1510.02298] [INSPIRE].
O. Hohm and B. Zwiebach, On the Riemann Tensor in Double Field Theory, JHEP 05 (2012) 126 [arXiv:1112.5296] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry I: Type II Theories, JHEP 11 (2011) 091 [arXiv:1107.1733] [INSPIRE].
D. Geissbuhler, Double Field Theory and N = 4 Gauged Supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].
G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of Double Field Theory, JHEP 11 (2011) 052 [Erratum ibid. 11 (2011) 109] [arXiv:1109.0290] [INSPIRE].
M. Graña and D. Marques, Gauged Double Field Theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].
D.S. Berman and K. Lee, Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions, Nucl. Phys. B 881 (2014) 369 [arXiv:1305.2747] [INSPIRE].
H. Lü, C.N. Pope and P.K. Townsend, Domain walls from anti-de Sitter space-time, Phys. Lett. B 391 (1997) 39 [hep-th/9607164] [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].
M.J. Duff, Hidden string symmetries?, Phys. Lett. B 173 (1986) 289 [INSPIRE].
N. Boulanger, E. Sezgin and P. Sundell, 4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius-Chern-Simons Gauge Theory, arXiv:1505.04957 [INSPIRE].
J. Gomis and H. Ooguri, Nonrelativistic closed string theory, J. Math. Phys. 42 (2001) 3127 [hep-th/0009181] [INSPIRE].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
J.-H. Park, Superfield theory and dual supermatrix models, JHEP 09 (2003) 046 [hep-th/0307060] [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: 1605.00403
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
Bekaert, X., Park, JH. Higher spin double field theory: a proposal. J. High Energ. Phys. 2016, 62 (2016). https://doi.org/10.1007/JHEP07(2016)062
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2016)062