Abstract
We construct an unfolded system for off-shell fields of arbitrary integer spin in 4d anti-de Sitter space. To this end we couple an on-shell system, encoding Fronsdal equations, to external Fronsdal currents for which we find an unfolded formulation. We present a reduction of the Fronsdal current system which brings it to the unfolded Fierz-Pauli system describing massive fields of arbitrary integer spin. Reformulating off-shell higher-spin system as the set of Schwinger–Dyson equations we compute propagators of higher-spin fields in the de Donder gauge directly from the unfolded equations. We discover operators that significantly simplify this computation, allowing a straightforward extraction of wave equations from an unfolded system.
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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, 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, Unfolded representation for relativistic equations in (2 + 1) anti-de Sitter space, Class. Quant. Grav. 11 (1994) 649 [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].
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].
E. Sezgin, E.D. Skvortsov and Y. Zhu, Chern-Simons Matter Theories and Higher Spin Gravity, JHEP 07 (2017) 133 [arXiv:1705.03197] [INSPIRE].
O.A. Gelfond and M.A. Vasiliev, Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations, Nucl. Phys. B 931 (2018) 383 [arXiv:1706.03718] [INSPIRE].
N. Misuna, On current contribution to Fronsdal equations, Phys. Lett. B 778 (2018) 71 [arXiv:1706.04605] [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].
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].
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].
E. Sezgin, P. Sundell,Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040].
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].
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].
M.A. Vasiliev, Actions, charges and off-shell fields in the unfolded dynamics approach, Int. J. Geom. Meth. Mod. Phys. 3 (2006) 37 [hep-th/0504090] [INSPIRE].
N.G. Misuna and M.A. Vasiliev, Off-Shell Scalar Supermultiplet in the Unfolded Dynamics Approach, JHEP 05 (2014) 140 [arXiv:1301.2230] [INSPIRE].
S.R. Das and A. Jevicki, Large N collective fields and holography, Phys. Rev. D 68 (2003) 044011 [hep-th/0304093] [INSPIRE].
A. Fotopoulos and M. Tsulaia, Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation, Int. J. Mod. Phys. A 24 (2009) 1 [arXiv:0805.1346] [INSPIRE].
A. Jevicki, K. Jin and Q. Ye, Collective Dipole Model of AdS/CFT and Higher Spin Gravity, J. Phys. A 44 (2011) 465402 [arXiv:1106.3983] [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].
N. Boulanger, N. Colombo and P. Sundell, A minimal BV action for Vasiliev’s four-dimensional higher spin gravity, JHEP 10 (2012) 043 [arXiv:1205.3339] [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].
I.L. Buchbinder and K. Koutrolikos, BRST Analysis of the Supersymmetric Higher Spin Field Models, JHEP 12 (2015) 106 [arXiv:1510.06569] [INSPIRE].
C. Arias, R. Bonezzi, N. Boulanger, E. Sezgin, P. Sundell, A. Torres-Gomez et al., Action principles for higher and fractional spin gravities, in International Workshop on Higher Spin Gauge Theories, (2017), pp. 213-253, DOI [arXiv:1603.04454] [INSPIRE].
S. Giombi and I.R. Klebanov, One Loop Tests of Higher Spin AdS/CFT, JHEP 12 (2013) 068 [arXiv:1308.2337] [INSPIRE].
S. Giombi, I.R. Klebanov and B.R. Safdi, Higher Spin AdSd+1/CFTd at One Loop, Phys. Rev. D 89 (2014) 084004 [arXiv:1401.0825] [INSPIRE].
A. Jevicki, K. Jin and J. Yoon, 1/N and loop corrections in higher spin AdS4/CFT3 duality, Phys. Rev. D 89 (2014) 085039 [arXiv:1401.3318] [INSPIRE].
S. Giombi, I.R. Klebanov and A.A. Tseytlin, Partition Functions and Casimir Energies in Higher Spin AdSd+1/CFTd , Phys. Rev. D 90 (2014) 024048 [arXiv:1402.5396] [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. Beccaria and A.A. Tseytlin, On higher spin partition functions, J. Phys. A 48 (2015) 275401 [arXiv:1503.08143] [INSPIRE].
M. Günaydin, E.D. Skvortsov and T. Tran, Exceptional F (4) higher-spin theory in AdS6 at one-loop and other tests of duality, JHEP 11 (2016) 168 [arXiv:1608.07582] [INSPIRE].
Y. Pang, E. Sezgin and Y. Zhu, One Loop Tests of Supersymmetric Higher Spin AdS4/CFT3 , Phys. Rev. D 95 (2017) 026008 [arXiv:1608.07298] [INSPIRE].
S. Giombi, I.R. Klebanov and Z.M. Tan, The ABC of Higher-Spin AdS/CFT, Universe 4 (2018) 18 [arXiv:1608.07611] [INSPIRE].
E.D. Skvortsov and T. Tran, AdS/CFT in Fractional Dimension and Higher Spin Gravity at One Loop, Universe 3 (2017) 61 [arXiv:1707.00758] [INSPIRE].
D. Ponomarev and A.A. Tseytlin, On quantum corrections in higher-spin theory in flat space, JHEP 05 (2016) 184 [arXiv:1603.06273] [INSPIRE].
S. Giombi, C. Sleight and M. Taronna, Spinning AdS Loop Diagrams: Two Point Functions, JHEP 06 (2018) 030 [arXiv:1708.08404] [INSPIRE].
C. Sleight and M. Taronna, Feynman rules for higher-spin gauge fields on AdSd+1 , JHEP 01 (2018) 060 [arXiv:1708.08668] [INSPIRE].
D. Ponomarev, E. Sezgin and E. Skvortsov, On one loop corrections in higher spin gravity, JHEP 11 (2019) 138 [arXiv:1904.01042] [INSPIRE].
B. Nagaraj and D. Ponomarev, Spinor-Helicity Formalism for Massless Fields in AdS4 , Phys. Rev. Lett. 122 (2019) 101602 [arXiv:1811.08438] [INSPIRE].
R. de Mello Koch, A. Jevicki, K. Suzuki and J. Yoon, AdS Maps and Diagrams of Bi-local Holography, JHEP 03 (2019) 133 [arXiv:1810.02332] [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].
B. Nagaraj and D. Ponomarev, Spinor-helicity formalism for massless fields in AdS4 III: contact four-point amplitudes, JHEP 08 (2020) 012 [arXiv:2004.07989] [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].
D. Ponomarev, Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure, JHEP 12 (2016) 117 [arXiv:1611.00361] [INSPIRE].
D. Ponomarev, Chiral Higher Spin Theories and Self-Duality, JHEP 12 (2017) 141 [arXiv:1710.00270] [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 and T. Tran, One-loop Finiteness of Chiral Higher Spin Gravity, JHEP 07 (2020) 021 [arXiv:2004.10797] [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].
N. Misuna, On unfolded off-shell formulation for higher-spin theory, Phys. Lett. B 798 (2019) 134956 [arXiv:1905.06925] [INSPIRE].
Y.M. Zinoviev, Frame-like gauge invariant formulation for massive high spin particles, Nucl. Phys. B 808 (2009) 185 [arXiv:0808.1778] [INSPIRE].
D.S. Ponomarev and M.A. Vasiliev, Frame-Like Action and Unfolded Formulation for Massive Higher-Spin Fields, Nucl. Phys. B 839 (2010) 466 [arXiv:1001.0062] [INSPIRE].
I.L. Buchbinder, T.V. Snegirev and Y.M. Zinoviev, Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS3 space, Phys. Lett. B 716 (2012) 243 [arXiv:1207.1215] [INSPIRE].
Y.M. Zinoviev, Massive higher spins in d = 3 unfolded, J. Phys. A 49 (2016) 095401 [arXiv:1509.00968] [INSPIRE].
I.L. Buchbinder, T.V. Snegirev and Y.M. Zinoviev, Unfolded equations for massive higher spin supermultiplets in AdS3 , JHEP 08 (2016) 075 [arXiv:1606.02475] [INSPIRE].
I.L. Buchbinder, M.V. Khabarov, T.V. Snegirev and Y.M. Zinoviev, Lagrangian formulation of the massive higher spin N = 1 supermultiplets in AdS4 space, Nucl. Phys. B 942 (2019) 1 [arXiv:1901.09637] [INSPIRE].
M.V. Khabarov and Y.M. Zinoviev, Massive higher spin fields in the frame-like multispinor formalism, Nucl. Phys. B 948 (2019) 114773 [arXiv:1906.03438] [INSPIRE].
M.V. Khabarov and Y.M. Zinoviev, Massive higher spin supermultiplets unfolded, Nucl. Phys. B 953 (2020) 114959 [arXiv:2001.07903] [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].
S.L. Lyakhovich and A.A. Sharapov, Schwinger-Dyson equation for non-Lagrangian field theory, JHEP 02 (2006) 007 [hep-th/0512119] [INSPIRE].
D.S. Kaparulin, S.L. Lyakhovich and A.A. Sharapov, On Lagrange structure of unfolded field theory, Int. J. Mod. Phys. A 26 (2011) 1347 [arXiv:1012.2567] [INSPIRE].
D.S. Kaparulin, S.L. Lyakhovich and A.A. Sharapov, Lagrange Anchor and Characteristic Symmetries of Free Massless Fields, SIGMA 8 (2012) 021 [arXiv:1112.1860] [INSPIRE].
O.V. Shaynkman and M.A. Vasiliev, Scalar field in any dimension from the higher spin gauge theory perspective, Theor. Math. Phys. 123 (2000) 683 [hep-th/0003123] [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].
C.P. Burgess, C.A. Lütken,Propagators and effective potentials in anti-de Sitter space, Phys. Lett. B 153 (1985) 137.
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Misuna, N. Off-shell higher-spin fields in AdS4 and external currents. J. High Energ. Phys. 2021, 172 (2021). https://doi.org/10.1007/JHEP12(2021)172
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DOI: https://doi.org/10.1007/JHEP12(2021)172