Abstract
Two-dimensional BF theory with infinitely many higher spin fields is proposed. It is interpreted as the AdS 2 higher spin gravity model describing a consistent interaction between local fields in AdS 2 space including gravitational field, higher spin partially-massless fields, and dilaton fields. We carry out analysis of the frame-like and the metric-like formulation of the theory. Infinite-dimensional higher spin global algebras and their finite-dimensional truncations are realized in terms of o(2, 1) − sp(2) Howe dual auxiliary variables.
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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].
S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Elements of Vasiliev theory, arXiv:1401.2975 [INSPIRE].
A.K.H. Bengtsson and I. Bengtsson, Higher ‘Spins’ in One and Two Space-time Dimensions, Phys. Lett. B 174 (1986) 294 [INSPIRE].
E.S. Fradkin and V.Y. Linetsky, Higher Spin Symmetry in One-dimension and Two-dimensions. 1., Mod. Phys. Lett. A 4 (1989) 2635 [INSPIRE].
M.A. Vasiliev, Higher spin gauge interactions for matter fields in two-dimensions, Phys. Lett. B 363 (1995) 51 [hep-th/9511063] [INSPIRE].
S.-J. Rey, News from Higher Spins: W ∞ , Black Holes and Entropy, talk given at the workshop Higher spins and holography, Simons center, March 2011.
K.B. Alkalaev, On higher spin extension of the Jackiw-Teitelboim gravity model, J. Phys. A 47 (2014) 365401 [arXiv:1311.5119] [INSPIRE].
D. Grumiller, M. Leston and D. Vassilevich, Anti-de Sitter holography for gravity and higher spin theories in two dimensions, Phys. Rev. D 89 (2014) 044001 [arXiv:1311.7413] [INSPIRE].
M.P. Blencowe, A Consistent Interacting Massless Higher Spin Field Theory in D = (2 + 1), Class. Quant. Grav. 6 (1989) 443 [INSPIRE].
E. Bergshoeff, M. Blencowe, and K. Stelle, Area Preserving Diffeomorphisms and Higher Spin Algebra, Commun. Math. Phys. 128 (1990) 213.
M. Henneaux and S.-J. Rey, Nonlinear W inf inity as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [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].
J.M.F. Labastida, M. Pernici and E. Witten, Topological Gravity in Two-Dimensions, Nucl. Phys. B 310 (1988) 611 [INSPIRE].
D. Montano and J. Sonnenschein, The Topology of Moduli Space and Quantum Field Theory, Nucl. Phys. B 324 (1989) 348 [INSPIRE].
E.P. Verlinde and H.L. Verlinde, A Solution of Two-dimensional Topological Quantum Gravity, Nucl. Phys. B 348 (1991) 457 [INSPIRE].
K. Li, Construction of topological W(3) gravity, Phys. Lett. B 251 (1990) 54 [INSPIRE].
B.M. Barbashov, V.V. Nesterenko and A.M. Chervyakov, The solitons in some geometrical field theories, Theor. Math. Phys. 40 (1979) 572 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
R. Jackiw, in Quantum theory of Gravity, S. Christansen ed., Hilger, Bristol, 1984.
T. Fukuyama and K. Kamimura, Gauge Theory of Two-dimensional Gravity, Phys. Lett. B 160 (1985) 259 [INSPIRE].
K. Isler and C.A. Trugenberger, A Gauge Theory of Two-dimensional Quantum Gravity, Phys. Rev. Lett. 63 (1989) 834 [INSPIRE].
A.H. Chamseddine and D. Wyler, Topological Gravity in (1 + 1)-dimensions, Nucl. Phys. B 340 (1990) 595 [INSPIRE].
S. Deser and R.I. Nepomechie, Anomalous Propagation of Gauge Fields in Conformally Flat Spaces, Phys. Lett. B 132 (1983) 321 [INSPIRE].
S. Deser and R.I. Nepomechie, Gauge Invariance Versus Masslessness in de Sitter Space, Annals Phys. 154 (1984) 396 [INSPIRE].
S. Deser and A. Waldron, Partial masslessness of higher spins in (A)dS, Nucl. Phys. B 607 (2001) 577 [hep-th/0103198] [INSPIRE].
Y. Zinoviev, On massive high spin particles in AdS, hep-th/0108192 [INSPIRE].
E.D. Skvortsov and M.A. Vasiliev, Geometric formulation for partially massless fields, Nucl. Phys. B 756 (2006) 117 [hep-th/0601095] [INSPIRE].
Y. Zinoviev, On massive spin 2 interactions, Nucl. Phys. B 770 (2007) 83 [hep-th/0609170] [INSPIRE].
R.R. Metsaev, Gravitational and higher-derivative interactions of massive spin 5/2 field in (A)dS space, Phys. Rev. D 77 (2008) 025032 [hep-th/0612279] [INSPIRE].
I.L. Buchbinder, T.V. Snegirev, Y. Zinoviev and Y. Zinoviev, Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS 3 space, Phys. Lett. B 716 (2012) 243 [arXiv:1207.1215] [INSPIRE].
E. Joung, L. Lopez and M. Taronna, On the cubic interactions of massive and partially-massless higher spins in (A)dS, JHEP 07 (2012) 041 [arXiv:1203.6578] [INSPIRE].
N. Boulanger, D. Ponomarev and E.D. Skvortsov, Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space, JHEP 05 (2013) 008 [arXiv:1211.6979] [INSPIRE].
B.L. Feigin, Lie algebras gl(λ) and cohomologies of Lie algebras of differential operators, Russian Math. Surv. 43 (1988) 169.
M.A. Vasiliev, Quantization on sphere and high spin superalgebras, JETP Lett. 50 (1989) 374 [INSPIRE].
C.N. Pope, L.J. Romans and X. Shen, W (infinity) and the Racah-wigner Algebra, Nucl. Phys. B 339 (1990) 191 [INSPIRE].
E. Joung and K. Mkrtchyan, Notes on higher-spin algebras: minimal representations and structure constants, JHEP 05 (2014) 103 [arXiv:1401.7977] [INSPIRE].
C.R. Nappi, Some Properties of an Analog of the Nonlinear σ Model, Phys. Rev. D 21 (1980) 418 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Quantum Equivalence of Dual Field Theories, Annals Phys. 162 (1985) 31 [INSPIRE].
M.G. Eastwood, Higher symmetries of the Laplacian, Annals Math. 161 (2005) 1645 [hep-th/0206233] [INSPIRE].
M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [INSPIRE].
M.A. Vasiliev, Higher spin superalgebras in any dimension and their representations, JHEP 12 (2004) 046 [hep-th/0404124] [INSPIRE].
T. Hartman and A. Strominger, Central Charge for AdS 2 Quantum Gravity, JHEP 04 (2009) 026 [arXiv:0803.3621] [INSPIRE].
M.A. Vasiliev, Cubic interactions of bosonic higher spin gauge fields in AdS 5, Nucl. Phys. B 616 (2001) 106 [Erratum ibid. B 652 (2003) 407] [hep-th/0106200] [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].
E.D. Skvortsov, Gauge fields in (A)dS(d) within the unfolded approach: algebraic aspects, JHEP 01 (2010) 106 [arXiv:0910.3334] [INSPIRE].
R. Jackiw, Gauge theories for gravity on a line, Theor. Math. Phys. 92 (1992) 979 [hep-th/9206093] [INSPIRE].
A. Kapustin and N. Seiberg, Coupling a QFT to a TQFT and Duality, JHEP 04 (2014) 001 [arXiv:1401.0740] [INSPIRE].
S.E. Konstein and M.A. Vasiliev, Extended Higher Spin Superalgebras and Their Massless Representations, Nucl. Phys. B 331 (1990) 475 [INSPIRE].
X. Bekaert, Higher spin algebras as higher symmetries, arXiv:0704.0898 [INSPIRE].
N. Boulanger, D. Ponomarev, E.D. Skvortsov and M. Taronna, On the uniqueness of higher-spin symmetries in AdS and CFT, Int. J. Mod. Phys. A 28 (2013) 1350162 [arXiv:1305.5180] [INSPIRE].
F.A. Bais, T. Tjin and P. van Driel, Covariantly coupled chiral algebras, Nucl. Phys. B 357 (1991) 632 [INSPIRE].
R. Howe, Transcending classical invariant theory, J. Amer. Math. Soc. 3 (1989) 2.
K.B. Alkalaev, On manifestly sp(2) invariant formulation of quadratic higher spin Lagrangians, JHEP 06 (2008) 081 [arXiv:0711.3639] [INSPIRE].
E. Bergshoeff, B. de Wit and M.A. Vasiliev, The Structure of the superW(infinity) (lambda) algebra, Nucl. Phys. B 366 (1991) 315 [INSPIRE].
E. Sezgin and P. Sundell, Doubletons and 5 − D higher spin gauge theory, JHEP 09 (2001) 036 [hep-th/0105001] [INSPIRE].
E. Sezgin and P. Sundell, 7 − D bosonic higher spin theory: Symmetry algebra and linearized constraints, Nucl. Phys. B 634 (2002) 120 [hep-th/0112100] [INSPIRE].
K.B. Alkalaev and M.A. Vasiliev, N = 1 supersymmetric theory of higher spin gauge fields in AdS 5 at the cubic level, Nucl. Phys. B 655 (2003) 57 [hep-th/0206068] [INSPIRE].
A. Sagnotti, E. Sezgin and P. Sundell, On higher spins with a strong Sp(2,R) condition, hep-th/0501156 [INSPIRE].
K. Alkalaev, FV-type action for AdS 5 mixed-symmetry fields, JHEP 03 (2011) 031 [arXiv:1011.6109] [INSPIRE].
M.A. Vasiliev, Extended Higher Spin Superalgebras and Their Realizations in Terms of Quantum Operators, Fortsch. Phys. 36 (1988) 33 [INSPIRE].
R. Jackiw, Gauge covariant conformal transformations, Phys. Rev. Lett. 41 (1978) 1635 [INSPIRE].
H. Afshar, A. Bagchi, R. Fareghbal, D. Grumiller and J. Rosseel, Spin-3 Gravity in Three-Dimensional Flat Space, Phys. Rev. Lett. 111 (2013) 121603 [arXiv:1307.4768] [INSPIRE].
H.A. Gonzalez, J. Matulich, M. Pino and R. Troncoso, Asymptotically flat spacetimes in three-dimensional higher spin gravity, JHEP 09 (2013) 016 [arXiv:1307.5651] [INSPIRE].
X. Bekaert and M. Grigoriev, Higher order singletons, partially massless fields and their boundary values in the ambient approach, Nucl. Phys. B 876 (2013) 667 [arXiv:1305.0162] [INSPIRE].
N. Boulanger, P. Sundell and M. Valenzuela, Three-dimensional fractional-spin gravity, JHEP 02 (2014) 052 [arXiv:1312.5700] [INSPIRE].
C.G. Callan Jr., S.B. Giddings, J.A. Harvey and A. Strominger, Evanescent black holes, Phys. Rev. D 45 (1992) 1005 [hep-th/9111056] [INSPIRE].
D. Cangemi and R. Jackiw, Gauge invariant formulations of lineal gravity, Phys. Rev. Lett. 69 (1992) 233 [hep-th/9203056] [INSPIRE].
D. Cangemi and R. Jackiw, Geometric gravitational forces on particles moving in a line, Phys. Lett. B 299 (1993) 24 [hep-th/9210036] [INSPIRE].
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Alkalaev, K.B. Global and local properties of AdS 2 higher spin gravity. J. High Energ. Phys. 2014, 122 (2014). https://doi.org/10.1007/JHEP10(2014)122
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DOI: https://doi.org/10.1007/JHEP10(2014)122