Towards metric-like higher spin gauge theories in three dimensions

We consider the coupling of a symmetric spin-3 gauge field φμνρ to three-dimensional gravity in a second-order metric-like formulation. The action that corresponds to an SL(3,R)×SL(3,R)?> Chern–Simons theory in the frame-like formulation is identified to quadratic order in the spin-3 field. We apply our result to compute corrections to the area law for higher spin black holes using Wald’s entropy formula. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

[1]  T. V. Snegirev,et al.  On gravitational interactions for massive higher spins in AdS3 , 2012, 1208.0183.

[2]  R. Gopakumar,et al.  Minimal model holography , 2012, 1207.6697.

[3]  E. Joung,et al.  Solving the Noether procedure for cubic interactions of higher spins in (A)dS , 2012, 1207.5520.

[4]  Ricardo Troncoso,et al.  Higher spin gravity in 3D: Black holes, global charges and thermodynamics , 2012, 1207.2844.

[5]  S. Theisen,et al.  The action for higher spin black holes in three dimensions , 2012, 1204.5105.

[6]  M. Grigoriev.  Parent formulations, frame-like Lagrangians, and generalized auxiliary fields , 2012, 1204.1793.

[7]  Thomas Hartman,et al.  Higher spin black holes from CFT , 2012, Journal of High Energy Physics.

[8]  P. Dempster,et al.  On the structure of quartic vertices for massless higher spin fields on Minkowski background , 2012, 1203.5597.

[9]  Thomas Hartman,et al.  Higher spin black holes from CFT , 2012, 1203.0015.

[10]  E. Hijano,et al.  Black holes and singularity resolution in higher spin gravity , 2012, Journal of High Energy Physics.

[11]  M. Vasiliev.  Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)dS_d$ , 2011, 1108.5921.

[12]  M. Taronna.  Higher-spin interactions: four-point functions and beyond , 2011, 1107.5843.

[13]  X. Bekaert,et al.  How higher-spin gravity surpasses the spin-two barrier , 2010, 1007.0435.

[14]  A. Sagnotti.  Notes on strings and higher spins , 2011, 1112.4285.

[15]  A. Campoleoni.  Higher Spins in D = 2 + 1 , 2011, 1110.5841.

[16]  E. Hijano,et al.  Black holes and singularity resolution in higher spin gravity , 2011, 1110.4117.

[17]  Eric Perlmutter,et al.  Partition functions of higher spin black holes and their CFT duals , 2011, 1108.2567.

[18]  Eric Perlmutter,et al.  Spacetime geometry in higher spin gravity , 2011, 1106.4788.

[19]  Per Kraus,et al.  Higher spin black holes , 2011, 1103.4304.

[20]  Thomas Hartman,et al.  Symmetries of holographic minimal models , 2011, 1101.2910.

[21]  R. Gopakumar,et al.  An AdS_3 Dual for Minimal Model CFTs , 2010, 1011.2986.

[22]  D. Polyakov.  Higher spins and open strings: Quartic interactions , 2010, 1011.0353.

[23]  A. Sagnotti,et al.  String Lessons for Higher-Spin Interactions , 2010, 1006.5242.

[24]  S. Pfenninger,et al.  Asymptotic W-symmetries in three-dimensional higher-spin gauge theories , 2011 .

[25]  S. Pfenninger,et al.  Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields , 2010, 1008.4744.

[26]  K. Mkrtchyan,et al.  General trilinear interaction for arbitrary even higher spin gauge fields , 2010, 1003.2877.

[27]  A. Sagnotti.  Higher Spins and Current Exchanges , 2010, 1002.3388.

[28]  X. Bekaert,et al.  Strong obstruction of the Berends–Burgers–van Dam spin-3 vertex , 2010, 1002.0289.

[29]  D. Francia.  On the relation between local and geometric Lagrangians for higher spins , 2010, 1001.3854.

[30]  X. Bekaert.  COMMENTS ON HIGHER-SPIN SYMMETRIES , 2008, 0807.4223.

[31]  A. Stahl,et al.  Physics at BES_III , 2008, 0809.1869.

[32]  N. Boulanger,et al.  On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory , 2008, 0805.2764.

[33]  V. Zhuravlov,et al.  Physics at BES-III , 2008, 0805.1346.

[34]  A. Sagnotti,et al.  Current Exchanges and Unconstrained Higher Spins , 2007, hep-th/0701163.

[35]  R. R. Metsaev.  BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields , 2005, hep-th/0512342.

[36]  M. Vasiliev,et al.  Nonlinear higher spin theories in various dimensions , 2005, hep-th/0503128.

[37]  G. Barnich,et al.  Parent Field Theory and Unfolding in BRST First-Quantized Terms , 2004, hep-th/0406192.

[38]  M. Vasiliev.  Nonlinear equations for symmetric massless higher spin fields in (A)dSd , 2003 .

[39]  M.A.Vasiliev.  Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)dS_d$ , 2003, hep-th/0304049.

[40]  A. Sagnotti,et al.  Free geometric equations for higher spins , 2002, hep-th/0207002.

[41]  M. Vasiliev,et al.  Higher-spin gauge interactions for massive matter fields in 3D AdS space-time , 1998, hep-th/9806236.

[42]  R. Wald,et al.  Black hole entropy is Noether charge. , 1993, Physical review. D, Particles and fields.

[43]  Zanelli,et al.  Geometry of the 2+1 black hole. , 1993, Physical review. D, Particles and fields.

[44]  Zanelli,et al.  Black hole in three-dimensional spacetime. , 1992, Physical review letters.

[45]  M. Vasiliev.  Consistent equations for interacting gauge fields of all spins in 3+1 dimensions , 1990 .

[46]  M. Blencowe,et al.  Area-preserving diffeomorphisms and higher-spin algebras , 1990 .

[47]  M. Blencowe.  A consistent interacting massless higher-spin field theory in D=2+1 , 1989 .

[48]  M P Blencowe.  A consistent interacting massless higher-spin field theory in D=2+1 , 1989 .

[49]  Edward Witten,et al.  (2+1)-Dimensional Gravity as an Exactly Soluble System , 1988 .

[50]  T. Damour,et al.  'Geometry' of Spin 3 Gauge Theories , 1987 .

[51]  E. Fradkin,et al.  Cubic interaction in extended theories of massless higher-spin fields , 1987 .

[52]  L. Brink,et al.  Cubic interaction terms for arbitrary spin , 1983 .

[53]  S. Deser,et al.  Consistency problems of spin-2-gravity coupling , 1980 .

[54]  D. Freedman,et al.  Systematics of Higher Spin Gauge Fields , 1980 .

[55]  C. Frønsdal.  Singletons and massless, integral-spin fields on de Sitter space , 1979 .

[56]  C. Frønsdal.  Massless Fields with Integer Spin , 1978 .