Advertisement

Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra

  • Patrick Concha
  • Nelson Merino
  • Olivera Miskovic
  • Evelyn Rodríguez
  • Patricio Salgado-Rebolledo
  • Omar Valdivia
Open Access
Regular Article - Theoretical Physics
  • 7 Downloads

Abstract

We study a three-dimensional Chern-Simons gravity theory based on the Maxwell algebra. We find that the boundary dynamics is described by an enlargement and deformation of the bms3 algebra with three independent central charges. This symmetry arises from a gravity action invariant under the local Maxwell group and is characterized by presence of Abelian generators which modify the commutation relations of the super-translations in the standard bms3 algebra. Our analysis is based on the charge algebra of the theory in the BMS gauge, which includes the known solutions of standard asymptotically flat case. The field content of the theory is different than the one of General Relativity, but it includes all its geometries as particular solutions. In this line, we also study the stationary solutions of the theory in ADM form and we show that the vacuum energy and the vacuum angular momentum of the stationary configuration are influenced by the presence of the gravitational Maxwell field.

Keywords

Conformal and W Symmetry Space-Time Symmetries Gauge-gravity correspondence Classical Theories of Gravity 

Notes

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.

References

  1. [1]
    M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    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 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    M. Henneaux, C. Martinez and R. Troncoso, Asymptotically anti-de Sitter spacetimes in topologically massive gravity, Phys. Rev. D 79 (2009) 081502 [arXiv:0901.2874] [INSPIRE].ADSMathSciNetGoogle Scholar
  4. [4]
    K. Skenderis, M. Taylor and B.C. van Rees, Topologically Massive Gravity and the AdS/CFT Correspondence, JHEP 09 (2009) 045 [arXiv:0906.4926] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    H. Afshar, B. Cvetkovic, S. Ertl, D. Grumiller and N. Johansson, Conformal Chern-Simons holographylock, stock and barrel, Phys. Rev. D 85 (2012) 064033 [arXiv:1110.5644] [INSPIRE].ADSGoogle Scholar
  6. [6]
    A. Sinha, On the new massive gravity and AdS/CFT, JHEP 06 (2010) 061 [arXiv:1003.0683] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    G. Compère, W. Song and A. Strominger, New Boundary Conditions for AdS3, JHEP 05 (2013) 152 [arXiv:1303.2662] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  8. [8]
    C. Troessaert, Enhanced asymptotic symmetry algebra of AdS 3, JHEP 08 (2013) 044 [arXiv:1303.3296] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    A. Pérez, D. Tempo and R. Troncoso, Boundary conditions for General Relativity on AdS 3 and the KdV hierarchy, JHEP 06 (2016) 103 [arXiv:1605.04490] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  10. [10]
    D. Grumiller and M. Riegler, Most general AdS 3 boundary conditions, JHEP 10 (2016) 023 [arXiv:1608.01308] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  11. [11]
    G. Barnich and G. Compère, Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions, Class. Quant. Grav. 24 (2007) F15 [gr-qc/0610130] [INSPIRE].
  12. [12]
    H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
  13. [13]
    R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    A. Ashtekar, J. Bicak and B.G. Schmidt, Asymptotic structure of symmetry reduced general relativity, Phys. Rev. D 55 (1997) 669 [gr-qc/9608042] [INSPIRE].
  15. [15]
    G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    A. Bagchi and R. Fareghbal, BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries, JHEP 10 (2012) 092 [arXiv:1203.5795] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    G. Barnich, A. Gomberoff and H.A. Gonzalez, The flat limit of three dimensional asymptotically anti-de Sitter spacetimes, Phys. Rev. D 86 (2012) 024020 [arXiv:1204.3288] [INSPIRE].ADSGoogle Scholar
  18. [18]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    G. Barnich and H.A. Gonzalez, Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity, JHEP 05 (2013) 016 [arXiv:1303.1075] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    R.N. Caldeira Costa, Aspects of the zero Λ limit in the AdS/CFT correspondence, Phys. Rev. D 90 (2014) 104018 [arXiv:1311.7339] [INSPIRE].ADSGoogle Scholar
  21. [21]
    R. Fareghbal and A. Naseh, Flat-Space Energy-Momentum Tensor from BMS/GCA Correspondence, JHEP 03 (2014) 005 [arXiv:1312.2109] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    C. Krishnan, A. Raju and S. Roy, A Grassmann path from AdS 3 to flat space, JHEP 03 (2014) 036 [arXiv:1312.2941] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    C. Duval, G.W. Gibbons and P.A. Horvathy, Conformal Carroll groups and BMS symmetry, Class. Quant. Grav. 31 (2014) 092001 [arXiv:1402.5894] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    G. Barnich, Entropy of three-dimensional asymptotically flat cosmological solutions, JHEP 10 (2012) 095 [arXiv:1208.4371] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    G. Barnich, L. Donnay, J. Matulich and R. Troncoso, Asymptotic symmetries and dynamics of three-dimensional flat supergravity, JHEP 08 (2014) 071 [arXiv:1407.4275] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    R. Basu, S. Detournay and M. Riegler, Spectral Flow in 3D Flat Spacetimes, JHEP 12 (2017) 134 [arXiv:1706.07438] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    O. Fuentealba, J. Matulich and R. Troncoso, Asymptotic structure of \( \mathcal{N}=2 \) supergravity in 3D: extended super-BMS 3 and nonlinear energy bounds, JHEP 09 (2017) 030 [arXiv:1706.07542] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  28. [28]
    C. Batlle, V. Campello and J. Gomis, Canonical realization of (2+1)-dimensional Bondi-Metzner-Sachs symmetry, Phys. Rev. D 96 (2017) 025004 [arXiv:1703.01833] [INSPIRE].ADSGoogle Scholar
  29. [29]
    S. Detournay and M. Riegler, Enhanced Asymptotic Symmetry Algebra of 2+1 Dimensional Flat Space, Phys. Rev. D 95 (2017) 046008 [arXiv:1612.00278] [INSPIRE].ADSMathSciNetGoogle Scholar
  30. [30]
    M.R. Setare and H. Adami, Enhanced asymptotic BMS 3 algebra of the flat spacetime solutions of generalized minimal massive gravity, Nucl. Phys. B 926 (2018) 70 [arXiv:1703.00936] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  31. [31]
    R. Schrader, The Maxwell group and the quantum theory of particles in classical homogeneous electromagnetic fields, Fortsch. Phys. 20 (1972) 701 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    H. Bacry, P. Combe and J.L. Richard, Group-theoretical analysis of elementary particles in an external electromagnetic field, Nuovo Cim. 67 (1970) 267.ADSCrossRefzbMATHGoogle Scholar
  33. [33]
    J. Gomis and A. Kleinschmidt, On free Lie algebras and particles in electro-magnetic fields, JHEP 07 (2017) 085 [arXiv:1705.05854] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    F. Izaurieta, E. Rodríguez and P. Salgado, Expanding Lie (super)algebras through Abelian semigroups, J. Math. Phys. 47 (2006) 123512 [hep-th/0606215] [INSPIRE].
  35. [35]
    P. Salgado and S. Salgado, \( \mathfrak{so}\left(D-1,1\right)\otimes \mathfrak{so}\left(D-1,2\right) \) algebras and gravity, Phys. Lett. B 728 (2014) 5 [INSPIRE].
  36. [36]
    J.A. de Azcarraga, K. Kamimura and J. Lukierski, Generalized cosmological term from Maxwell symmetries, Phys. Rev. D 83 (2011) 124036 [arXiv:1012.4402] [INSPIRE].ADSGoogle Scholar
  37. [37]
    S. Fedoruk and J. Lukierski, Maxwell group and HS field theory, J. Phys. Conf. Ser. 474 (2013) 012016 [arXiv:1309.6878] [INSPIRE].CrossRefGoogle Scholar
  38. [38]
    P. Salgado, R.J. Szabo and O. Valdivia, Topological gravity and transgression holography, Phys. Rev. D 89 (2014) 084077 [arXiv:1401.3653] [INSPIRE].ADSGoogle Scholar
  39. [39]
    S. Bonanos, J. Gomis, K. Kamimura and J. Lukierski, Maxwell Superalgebra and Superparticle in Constant Gauge Badkgrounds, Phys. Rev. Lett. 104 (2010) 090401 [arXiv:0911.5072] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    S. Hoseinzadeh and A. Rezaei-Aghdam, (2+1)-dimensional gravity from Maxwell and semisimple extension of the Poincaré gauge symmetric models, Phys. Rev. D 90 (2014) 084008 [arXiv:1402.0320] [INSPIRE].
  41. [41]
    P.K. Concha, O. Fierro, E.K. Rodríguez and P. Salgado, Chern-Simons supergravity in D = 3 and Maxwell superalgebra, Phys. Lett. B 750 (2015) 117 [arXiv:1507.02335] [INSPIRE].
  42. [42]
    P.K. Concha, R. Durka, N. Merino and E.K. Rodríguez, New family of Maxwell like algebras, Phys. Lett. B 759 (2016) 507 [arXiv:1601.06443] [INSPIRE].
  43. [43]
    P.K. Concha, O. Fierro and E.K. Rodríguez, Inönü-Wigner contraction and D = 2 + 1 supergravity, Eur. Phys. J. C 77 (2017) 48 [arXiv:1611.05018] [INSPIRE].
  44. [44]
    R. Caroca, P. Concha, O. Fierro, E. Rodríguez and P. Salgado-ReboLledó, Generalized Chern-Simons higher-spin gravity theories in three dimensions, Nucl. Phys. B 934 (2018) 240 [arXiv:1712.09975] [INSPIRE].
  45. [45]
    L. Avilés, E. Frodden, J. Gomis, D. Hidalgo and J. Zanelli, Non-Relativistic Maxwell Chern-Simons Gravity, JHEP 05 (2018) 047 [arXiv:1802.08453] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    A. Strominger, Asymptotic Symmetries of Yang-Mills Theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  48. [48]
    R. Caroca, P. Concha, E. Rodríguez and P. Salgado-ReboLledó, Generalizing the \( \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_3 \) and 2D-conformal algebras by expanding the Virasoro algebra, Eur. Phys. J. C 78 (2018) 262 [arXiv:1707.07209] [INSPIRE].
  49. [49]
    M. Bañados, Global charges in Chern-Simons field theory and the (2+1) black hole, Phys. Rev. D 52 (1996) 5816 [hep-th/9405171] [INSPIRE].Google Scholar
  50. [50]
    O. Mišković, R. Olea and D. Roy, Vacuum energy in asymptotically flat 2 + 1 gravity, Phys. Lett. B 767 (2017) 258 [arXiv:1610.06101] [INSPIRE].ADSMathSciNetGoogle Scholar
  51. [51]
    S. Detournay, D. Grumiller, F. Schöller and J. Simón, Variational principle and one-point functions in three-dimensional flat space Einstein gravity, Phys. Rev. D 89 (2014) 084061 [arXiv:1402.3687] [INSPIRE].ADSGoogle Scholar
  52. [52]
    M. Bañados and F. Mendez, A note on covariant action integrals in three-dimensions, Phys. Rev. D 58 (1998) 104014 [hep-th/9806065] [INSPIRE].ADSMathSciNetGoogle Scholar
  53. [53]
    O. Mišković and R. Olea, On boundary conditions in three-dimensional AdS gravity, Phys. Lett. B 640 (2006) 101 [hep-th/0603092] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  54. [54]
    B. Julia and S. Silva, Currents and superpotentials in classical gauge invariant theories. 1. Local results with applications to perfect fluids and general relativity, Class. Quant. Grav. 15 (1998) 2173 [gr-qc/9804029] [INSPIRE].
  55. [55]
    S.-S. Feng, B. Wang and X.-H. Meng, Conservative currents of boundary charges in AdS 2+1 gravity, Commun. Theor. Phys. 36 (2001) 33 [hep-th/9902108] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. [56]
    G. Compère and A. Fiorucci, Asymptotically flat spacetimes with BMS 3 symmetry, Class. Quant. Grav. 34 (2017) 204002 [arXiv:1705.06217] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  57. [57]
    T. Regge and C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Annals Phys. 88 (1974) 286 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  58. [58]
    R. Fareghbal and A. Naseh, Rindler/Contracted-CFT Correspondence, JHEP 06 (2014) 134 [arXiv:1404.3937] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Patrick Concha
    • 2
  • Nelson Merino
    • 3
  • Olivera Miskovic
    • 2
  • Evelyn Rodríguez
    • 4
  • Patricio Salgado-Rebolledo
    • 5
  • Omar Valdivia
    • 1
  1. 1.Facultad de Ingeniería y ArquitecturaUniversidad Arturo PratIquiqueChile
  2. 2.Instituto de FísicaPontificia Universidad Católica de ValparaísoValparaisoChile
  3. 3.APC, CNRS-Universitè Paris 7Paris CEDEX 13France
  4. 4.Departamento de Ciencias, Facultad de Artes LiberalesUniversidad Adolfo IbáñezViña del MarChile
  5. 5.Facultad de Ingeniería y Ciencias & UAI Physics CenterUniversidad Adolfo IbáñezSantiagoChile

Personalised recommendations