Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields

[en] We discuss the emergence of W-algebras as asymptotic symmetries of higher-spin gauge theories coupled to three-dimensional Einstein gravity with a negative cosmological constant. We focus on models involving a finite number of bosonic higher-spin fields, and especially on the example provided by the coupling of a spin-3 field to gravity. It is described by a SL(3) times SL(3) Chern-Simons theory and its asymptotic symmetry algebra is given by two copies of the classical W_3-algebra with central charge the one computed by Brown and Henneaux in pure gravity with negative cosmological constant.

Disciplines :

Physics

Author, co-author :

Campoleoni, Andrea

Fredenhagen, Stefan

Pfenninger, Stefan

Theisen, Stefan

Language :

English

Title :

Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields

Publication date :

04 November 2010

Journal title :

Journal of High Energy Physics

ISSN :

1126-6708

eISSN :

1029-8479

Publisher :

Springer, Heidelberg, Germany

Volume :

1011

Issue :

007

Pages :

1-35

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi UMONS :

since 04 December 2016

Statistics

Number of views

7 (0 by UMONS)

Number of downloads

0 (0 by UMONS)

More statistics

Scopus citations^®

462

Scopus citations^®
without self-citations

433

OpenCitations

337

OpenAlex citations

433

Bibliography

C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D 18 (1978) 3624 [SPIRES].
X. Bekaert, N. Boulanger and P. Sundell, How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples, arXiv:1007.0435 [SPIRES].
M.A. Vasiliev, Higher-spin gauge theories in four, three and two dimensions, Int. J. Mod. Phys. D 5 (1996) 763 [hep-th/9611024] [SPIRES].
X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [SPIRES].
C. Iazeolla, On the Algebraic Structure of Higher-Spin Field Equations and New Exact Solutions, arXiv:0807.0406 [SPIRES].
D. Francia and A. Sagnotti, On the geometry of higher-spin gauge fields, Class. Quant. Grav. 20 (2003) S473 [hep-th/0212185] [SPIRES].
D. Sorokin, Introduction to the classical theory of higher spins, AIP Conf. Proc. 767 (2005) 172 [hep-th/0405069] [SPIRES].
N. Bouatta, G. Compère and A. Sagnotti, An introduction to free higher-spin fields, hep-th/0409068 [SPIRES].
D. Francia and A. Sagnotti, Higher-spin geometry and string theory, J. Phys. Conf. Ser. 33 (2006) 57 [hep-th/0601199] [SPIRES].
A. Campoleoni, Metric-like Lagrangian Formulations for Higher-Spin Fields of Mixed Symmetry, Riv. Nuovo Cim. 033 (2010) 123 [arXiv:0910.3155] [SPIRES].
A. Sagnotti, E. Sezgin and P. Sundell, On higher spins with a strong Sp(2,R) condition, hep-th/0501156 [SPIRES].
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] [SPIRES].
C. Aragone and S. Deser, Consistency Problems of Hypergravity, Phys. Lett. B 86 (1979) 161 [SPIRES].
C. Aragone and S. Deser, Hypersymmetry In D = 3 Of Coupled Gravity Massless Spin 5/2 System, Class. Quant. Grav. 1 (1984) L9 [SPIRES].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 243 (1990) 378 [SPIRES].
M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [SPIRES].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [SPIRES].
M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [SPIRES].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [gr-qc/9302012] [SPIRES].
A. Strominger, Black hole entropy from near-horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [SPIRES].
P. Bouwknegt and K. Schoutens, W symmetry in conformal field theory, Phys. Rept. 223 (1993) 183 [hep-th/9210010] [SPIRES].
A. Achúcarro and P.K. Townsend, A Chern-Simons Action for Three-Dimensional anti-de Sitter Supergravity Theories, Phys. Lett. B 180 (1986) 89 [SPIRES].
E. Witten, (2 + 1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [SPIRES].
M.P. Blencowe, A Consistent Interacting Massless Higher Spin Field Theory In D = (2 + 1), Class. Quant. Grav. 6 (1989) 443 [SPIRES].
E. Bergshoeff, M.P. Blencowe and K.S. Stelle, Area Preserving Diffeomorphisms And Higher Spin Algebra, Commun. Math. Phys. 128 (1990) 213 [SPIRES].
M.A. Vasiliev, Higher Spin Algebras And Quantization On The Sphere And Hyperboloid, Int. J. Mod. Phys. A 6 (1991) 1115 [SPIRES].
S.F. Prokushkin and M.A. Vasiliev, Higher-spin gauge interactions for massive matter fields in 3D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [SPIRES].
A. Bilal, V.V. Fock and I.I. Kogan, On the origin of W algebras, Nucl. Phys. B 359 (1991) 635 [SPIRES].
J. de Boer and J. Goeree, W gravity from Chern-Simons theory, Nucl. Phys. B 381 (1992) 329 [hep-th/9112060] [SPIRES].
J. Balog, L. Fehér, L. O'Raifeartaigh, P. Forgács and A. Wipf, Toda Theory And W Algebra From A Gauged WZNW Point Of View, Ann. Phys. 203 (1990) 76 [SPIRES].
M. Henneaux and S.-J. Rey, Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, arXiv:1008.4579 [SPIRES].
T. Curtright, Massless Field Supermultiplets With Arbitrary Spin, Phys. Lett. B 85 (1979) 219 [SPIRES].
C. Fronsdal, Singletons and Massless, Integral Spin Fields on de Sitter Space (Elementary Particles in a Curved Space VII), Phys. Rev. D 20 (1979) 848 [SPIRES].
B. Binegar, Relativistic Field Theories In Three-Dimensions, J. Math. Phys. 23 (1982) 1511 [SPIRES].
M.A. Vasiliev, 'Gauge' Form Of Description Of Massless Fields With Arbitrary Spin. (in Russian), Yad. Fiz. 32 (1980) 855
[Sov. J. Nucl. Phys. 32 (1980) 439] [SPIRES].
M.A. Vasiliev, Free Massless Fields Of Arbitrary Spin In The De Sitter Space And Initial Data For A Higher Spin Superalgebra, Fortsch. Phys. 35 (1987) 741
[Yad. Fiz. 45 (1987) 1784] [SPIRES].
V.E. Lopatin and M.A. Vasiliev, Free Massless Bosonic Fields Of Arbitrary Spin In d-dimensional de Sitter Space, Mod. Phys. Lett. A 3 (1988) 257 [SPIRES].
M. Hamermesh, Group theory and its applications to physical problems, Dover Publications, New York U.S.A. (1969).
E.S. Fradkin and M.A. Vasiliev, Candidate to the Role of Higher Spin Symmetry, Ann. Phys. 177 (1987) 63 [SPIRES].
J. Hoppe, Quantum theory of a massless relativistic surface and a two-dimensional bound state problem, Ph.D. Thesis, Massachusetts Institute of Technology, Massachusetts U.S.A. (1982).
A. Achúcarro and P.K. Townsend, Extended Supergravities In d = (2 + 1) As Chern-Simons Theories, Phys. Lett. B 229 (1989) 383 [SPIRES].
M. Bañados, Global charges in Chern-Simons field theory and the (2 + 1) black hole, Phys. Rev. D 52 (1996) 5816 [hep-th/9405171] [SPIRES].
M. Bañados, T. Brotz and M.E. Ortiz, Boundary dynamics and the statistical mechanics of the 2 + 1 dimensional black hole, Nucl. Phys. B 545 (1999) 340 [hep-th/9802076] [SPIRES].
M. Bañados, Three-dimensional quantum geometry and black holes, hep-th/9901148 [SPIRES].
S. Carlip, Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole, Class. Quant. Grav. 22 (2005) R85 [gr-qc/0503022] [SPIRES].
T. Regge and C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Ann. Phys. 88 (1974) 286 [SPIRES].
R. Benguria, P. Cordero and C. Teitelboim, Aspects of the Hamiltonian Dynamics of Interacting Gravitational Gauge and Higgs Fields with Applications to Spherical Symmetry, Nucl. Phys. B 122 (1977) 61 [SPIRES].
V.E. Didenko, A.S. Matveev and M.A. Vasiliev, BTZ black hole as solution of 3d higher spin gauge theory, Theor. Math. Phys. 153 (2007) 1487
[Teor. Mat. Fiz. 153 (2007) 158] [hep-th/0612161] [SPIRES].
K. Skenderis and S.N. Solodukhin, Quantum effective action from the AdS/CFT correspondence, Phys. Lett. B 472 (2000) 316 [hep-th/9910023] [SPIRES].
C. Fefferman and C. R. Graham, Conformal Invariants in Elie Cartan et les Mathématiques d'aujourd'hui, Astèrisque (1985).
O. Coussaert, M. Henneaux and P. van Driel, The Asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant, Class. Quant. Grav. 12 (1995) 2961 [gr-qc/9506019] [SPIRES].
M. Bañados, K. Bautier, O. Coussaert, M. Henneaux and M. Ortiz, Anti-de Sitter/CFT correspondence in three-dimensional supergravity, Phys. Rev. D 58 (1998) 085020 [hep-th/9805165] [SPIRES].
M. Henneaux, L. Maoz and A. Schwimmer, Asymptotic dynamics and asymptotic symmetries of three- dimensional extended AdS supergravity, Annals Phys. 282 (2000) 31 [hep-th/9910013] [SPIRES].
M. Henneaux and C. Teitelboim, Asymptotically anti-de Sitter Spaces, Commun. Math. Phys. 98 (1985) 391 [SPIRES].
P. Mathieu, Extended Classical Conformal Algebras and the Second Hamiltonian Structure of Lax Equations, Phys. Lett. B 208 (1988) 101 [SPIRES].
S. Okubo and J. Patera, General Indices Of Representations And Casimir Invariants, J. Math. Phys. 25 (1984) 219 [SPIRES].
C.N. Pope and P.K. Townsend, Conformal Higher Spin In (2 + 1)-Dimensions, Phys. Lett. B 225 (1989) 245 [SPIRES].
A.V. Razumov and M.V. Saveliev, Lie Algebras, Geometry, and Toda-type Systems, Cambridge Lecture Notes in Physics, Cambridge University Press, Cambridge U.K. (1997).
F.A. Bais, P. Bouwknegt, M. Surridge and K. Schoutens, Extensions of the Virasoro Algebra Constructed from Kac-Moody Algebras Using Higher Order Casimir Invariants, Nucl. Phys. B 304 (1988) 348 [SPIRES].
F.A. Bais, T. Tjin and P. van Driel, Covariantly coupled chiral algebras, Nucl. Phys. B 357 (1991) 632 [SPIRES].