Skip to main content
Download PDF

A remarkably simple theory of 3d massive gravity

Journal of High Energy Physics volume 2019, Article number: 91 (2019) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We propose and study a new action for three-dimensional massive gravity. This action takes a very simple form when written in terms of connection and triad variables, but the connection can also be integrated out to obtain a triad formulation. The quadratic action for the perturbations around a Minkowski background reproduces the action of self-dual massive gravity, in agreement with the expectation that the theory propagates a massive graviton. We confirm this result at the non-linear level with a Hamiltonian analysis, and show that this new theory does indeed possess a single massive degree of freedom. The action depends on four coupling constants, and we identify the various massive and topological (or massless) limits in the space of parameters. This richness, along with the simplicity of the action, opens a very interesting new window onto massive gravity.

References

  1. K. Hinterbichler, Theoretical aspects of massive gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].

    ADS  Article  Google Scholar 

  2. S.F. Hassan and R.A. Rosen, Bimetric gravity from ghost-free massive gravity, JHEP 02 (2012) 126 [arXiv:1109.3515] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. C. de Rham, Massive gravity, Living Rev. Rel. 17 (2014) 7 [arXiv:1401.4173] [INSPIRE].

    Article  MATH  Google Scholar 

  4. A. Schmidt-May and M. von Strauss, Recent developments in bimetric theory, J. Phys. A 49 (2016) 183001 [arXiv:1512.00021] [INSPIRE].

  5. C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].

    ADS  Article  Google Scholar 

  6. C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].

  7. D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].

  8. S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].

    ADS  Article  Google Scholar 

  9. S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372.

    ADS  MathSciNet  Article  Google Scholar 

  10. S.N. Solodukhin, Holography with gravitational Chern-Simons, Phys. Rev. D 74 (2006) 024015 [hep-th/0509148] [INSPIRE].

  11. W. Li, W. Song and A. Strominger, Chiral gravity in three dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  12. 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].

    ADS  MathSciNet  Article  Google Scholar 

  13. S. Alexander and N. Yunes, Chern-Simons modified general relativity, Phys. Rept. 480 (2009) 1 [arXiv:0907.2562] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  14. M. Crisostomi, K. Noui, C. Charmousis and D. Langlois, Beyond Lovelock gravity: higher derivative metric theories, Phys. Rev. D 97 (2018) 044034 [arXiv:1710.04531] [INSPIRE].

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

    ADS  MathSciNet  Article  Google Scholar 

  16. E. Bergshoeff et al., Minimal massive 3D gravity, Class. Quant. Grav. 31 (2014) 145008 [arXiv:1404.2867] [INSPIRE].

  17. E. Bergshoeff, W. Merbis, A.J. Routh and P.K. Townsend, The third way to 3D gravity, Int. J. Mod. Phys. D 24 (2015) 1544015 [arXiv:1506.05949] [INSPIRE].

  18. S. Deser and R. Jackiw, ‘Selfduality’ of topologically massive gauge theories, Phys. Lett. 139B (1984) 371.

  19. C. Aragone and A. Khoudeir, Selfdual massive gravity, Phys. Lett. B 173 (1986) 141 [INSPIRE].

  20. S. Deser and J.G. McCarthy, Selfdual formulations of D = 3 gravity theories, Phys. Lett. B 246 (1990) 441 [INSPIRE].

  21. K. Hinterbichler and R.A. Rosen, Interacting spin-2 fields, JHEP 07 (2012) 047 [arXiv:1203.5783] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  22. E.A. Bergshoeff et al., Zwei-Dreibein gravity: a two-frame-field model of 3D massive gravity, Phys. Rev. Lett. 111 (2013) 111102 [Erratum ibid. 111 (2013) 259902] [arXiv:1307.2774] [INSPIRE].

  23. S. Alexandrov and C. Deffayet, On partially massless theory in 3 dimensions, JCAP 03 (2015) 043 [arXiv:1410.2897] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  24. E.A. Bergshoeff et al., Chern-Simons-like gravity theories, Lect. Notes Phys. 892 (2015) 181 [arXiv:1402.1688].

    ADS  MathSciNet  Article  Google Scholar 

  25. W. Merbis, Chern-Simons-like theories of gravity, Ph.D. thesis, Groningen University, Groningen, The Netherlands (2014), arXiv:1411.6888 [INSPIRE].

  26. B. Li, T.P. Sotiriou and J.D. Barrow, f (T) gravity and local Lorentz invariance, Phys. Rev. D 83 (2011) 064035 [arXiv:1010.1041] [INSPIRE].

  27. N. Tamanini and C.G. Boehmer, Good and bad tetrads in f (T) gravity, Phys. Rev. D 86 (2012) 044009 [arXiv:1204.4593] [INSPIRE].

  28. D. Grumiller, P. Hacker and W. Merbis, Soft hairy warped black hole entropy, JHEP 02 (2018) 010 [arXiv:1711.07975] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  29. M. Geiller, Lorentz-diffeomorphism edge modes in 3d gravity, JHEP 02 (2018) 029 [arXiv:1712.05269] [INSPIRE].

  30. M. Geiller, Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity, Nucl. Phys. B 924 (2017) 312 [arXiv:1703.04748] [INSPIRE].

Download references

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.

Author information

Authors and Affiliations

  1. Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, UMR 5672, F-69342, Lyon, France

    Marc Geiller

  2. Institut Denis Poisson, Université de Tours, Université d’Orléans, CNRS, UMR 7013, 37200, Tours, France

    Karim Noui

  3. Laboratoire Astroparticule et Cosmologie, Université Paris Diderot, CNRS, UMR 7164, 75013, Paris, France

    Karim Noui

Authors
  1. Marc Geiller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karim Noui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marc Geiller.

Additional information

ArXiv ePrint: 1812.01018

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Geiller, M., Noui, K. A remarkably simple theory of 3d massive gravity. J. High Energ. Phys. 2019, 91 (2019). https://doi.org/10.1007/JHEP04(2019)091

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP04(2019)091

Keywords

  • Classical Theories of Gravity
  • Space-Time Symmetries