Skip to main content
Log in

Hamiltonian analysis of symmetries in a massive theory of gravity

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We construct the generator of hamiltonian gauge symmetries in a 2 + 1 dimensional massive theory of gravity, proposed recently, through a systematic off-shell algorithm. Using a field dependent map among gauge parameters we show that the symmetries obtained from this generator are on-shell equivalent to the Poincaré gauge symmetries. We also clarify certain subtle issues concerning the implementation of this map.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive gravity in three dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. E.A. Bergshoeff, O. Hohm and P.K. Townsend, More on massive 3D gravity, Phys. Rev. D 79 (2009) 124042 [arXiv:0905.1259] [ inSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. S. Deser, Ghost-free, finite, fourth order D =3 (alas) gravity, Phys. Rev. Lett. 103 (2009) 101302 [arXiv:0904.4473] [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. I. Oda, Renormalizability of massive gravity in three dimensions, JHEP 05 (2009) 064 [arXiv:0904.2833] [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. G. Clement, Warped AdS 3 black holes in new massive gravity, Class. Quant. Grav. 26 (2009) 105015 [arXiv:0902.4634] [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. I. Gullu, T.C. Sisman and B. Tekin, Canonical structure of higher derivative gravity in 3D, Phys. Rev. D 81 (2010) 104017 [arXiv:1002.3778] [ inSPIRE].

    MathSciNet  ADS  Google Scholar 

  7. I. Gullu, T. Cagri Sisman and B. Tekin, Born-Infeld extension of new massive gravity, Class. Quant. Grav. 27 (2010) 162001 [arXiv:1003.3935] [ inSPIRE].

    Article  ADS  Google Scholar 

  8. M. Blagojevic and B. Cvetkovic, Hamiltonian analysis of BHT massive gravity, JHEP 01 (2011) 082 [arXiv:1010.2596] [ inSPIRE].

    Article  ADS  Google Scholar 

  9. M. Blagojevic and B. Cvetkovic, Extra gauge symmetries in BHT gravity, JHEP 03 (2011) 139 [arXiv:1103.2388] [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. A. Perez, D. Tempo and R. Troncoso, Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity, JHEP 07 (2011) 093 [arXiv:1106.4849] [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. D.P. Jatkar and A. Sinha, New massive gravity and AdS 4 counterterms, Phys. Rev. Lett. 106 (2011) 171601 [arXiv:1101.4746] [ inSPIRE].

    Article  ADS  Google Scholar 

  12. H. Ahmedov and A.N. Aliev, Exact solutions in D-3 new massive gravity, Phys. Rev. Lett. 106 (2011) 021301 [arXiv:1006.4264] [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A 173 (1939) 211.

    MathSciNet  ADS  Google Scholar 

  14. S. Deser, R. Jackiw and S. Templeton, Three-Dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975 [ inSPIRE].

    Article  ADS  Google Scholar 

  15. S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. D. Dalmazi and E.L. Mendonca, Generalized soldering of + −2 helicity states in D = 2+ 1, Phys. Rev. D 80 (2009) 025017 [arXiv:0906.4531] [ inSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. E. Bergshoeff, O. Hohm and P. Townsend, On massive gravitons in 2 + 1 dimensions, J. Phys. Conf. Ser. 229 (2010) 012005 [arXiv:0912.2944] [ inSPIRE].

    Article  ADS  Google Scholar 

  18. M. Sadegh and A. Shirzad, Constraint strucrure of the three dimensional massive gravity, Phys. Rev. D 83 (2011) 084040 [arXiv:1010.2887] [ inSPIRE].

    ADS  Google Scholar 

  19. R. Utiyama, Invariant theoretical interpretation of interaction, Phys. Rev. 101 (1956) 1597 [ inSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. T. Kibble, Lorentz invariance and the gravitational field, J. Math. Phys. 2 (1961) 212 [ inSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. D.W. Sciama, On the analog between charge and spin in general relativity, in Recent developments in general relativity, festschrift for Leopold Infeld, Pergamon Press, New York U.S.A. (1962).

    Google Scholar 

  22. F. Hehl, P. Von Der Heyde, G. Kerlick and J. Nester, General relativity with spin and torsion: foundations and prospects, Rev. Mod. Phys. 48 (1976) 393 [ inSPIRE].

    Article  ADS  Google Scholar 

  23. M. Blagojevic, Gravitation and gauge symmetries, IOP, Bristol, U.K. (2002).

    Book  MATH  Google Scholar 

  24. L. Castellani, Symmetries in constrained hamiltonian systems, Annals Phys. 143 (1982) 357 [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. R. Banerjee, H. Rothe and K. Rothe, Hamiltonian approach to lagrangian gauge symmetries, Phys. Lett. B 463 (1999) 248 [hep-th/9906072] [ inSPIRE].

    MathSciNet  ADS  Google Scholar 

  26. R. Banerjee, H. Rothe and K. Rothe, Master equation for lagrangian gauge symmetries, Phys. Lett. B 479 (2000) 429 [hep-th/9907217] [ inSPIRE].

    MathSciNet  ADS  Google Scholar 

  27. M. Henneaux, C. Teitelboim and J. Zanelli, Gauge invariance and degree of freedom count, Nucl. Phys. B 332 (1990) 169 [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. R. Banerjee, P. Mukherjee and A. Saha, Interpolating action for strings and membranes: a study of symmetries in the constrained hamiltonian approach, Phys. Rev. D 70 (2004) 026006 [hep-th/0403065] [ inSPIRE].

    MathSciNet  ADS  Google Scholar 

  29. R. Banerjee, P. Mukherjee and A. Saha, Bosonic p-brane and A -D-M decomposition, Phys. Rev. D 72 (2005) 066015 [hep-th/0501030] [ inSPIRE].

    MathSciNet  ADS  Google Scholar 

  30. P. Mukherjee and A. Saha, Gauge invariances vis-a-vis diffeomorphisms in second order metric gravity, Int. J. Mod. Phys. A 24 (2009) 4305 [arXiv:0705.4358] [ inSPIRE].

    MathSciNet  ADS  Google Scholar 

  31. S. Gangopadhyay, A.G. Hazra and A. Saha, Noncommutativity in interpolating string: a study of gauge symmetries in noncommutative framework, Phys. Rev. D 74 (2006) 125023 [hep-th/0701012] [ inSPIRE].

    MathSciNet  ADS  Google Scholar 

  32. R. Banerjee, S. Gangopadhyay, P. Mukherjee and D. Roy, Symmetries of topological gravity with torsion in the hamiltonian and lagrangian formalisms, JHEP 02 (2010) 075 [arXiv:0912.1472] [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. G. Clement, Black holes with a null killing vector in new massive gravity in three dimensions, Class. Quant. Grav. 26 (2009) 165002 [arXiv:0905.0553] [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. J. Oliva, D. Tempo and R. Troncoso, Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity, JHEP 07 (2009) 011 [arXiv:0905.1545] [ inSPIRE].

    Article  ADS  Google Scholar 

  35. Y.S. Myung, Y.-W. Kim, T. Moon and Y.-J. Park, Classical stability of BTZ black hole in new massive gravity, Phys. Rev. D 84 (2011) 024044 [arXiv:1105.4205] [ inSPIRE].

    ADS  Google Scholar 

  36. P.A.M. Dirac, Lectures on quantum mechanics, Dover Publications, Dover U.K. (2001).

    Google Scholar 

  37. J. Gomis, M. Henneaux and J. Pons, Existence theorem for gauge symmetries in hamiltonian constrained systems, Class. Quant. Grav. 7 (1990) 1089 [ inSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. M. Blagojevic and B. Cvetkovic, Canonical structure of 3-D gravity with torsion, in Trends in GR andQC 2 (2006) 103, Ch. Benton ed., Nova Science, New York U.S.A. [gr-qc/0412134] [ inSPIRE].

  39. M. Blagojevic and B. Cvetkovic, Canonical structure of topologically massive gravity with a cosmological constant, JHEP 05 (2009) 073 [arXiv:0812.4742] [ inSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Debraj Roy.

Additional information

ArXiv ePrint: 1108.4591

Rights and permissions

Reprints and permissions

About this article

Cite this article

Banerjee, R., Gangopadhyay, S. & Roy, D. Hamiltonian analysis of symmetries in a massive theory of gravity. J. High Energ. Phys. 2011, 121 (2011). https://doi.org/10.1007/JHEP10(2011)121

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP10(2011)121

Keywords

Navigation