3D Born-Infeld gravity and supersymmetry

Open Access


We construct the most general parity-even higher-derivative \( \mathcal{N} \) = 1 off-shell supergravity model in three dimensions with a maximum of six derivatives. Excluding terms quadratic in the curvature tensor with two explicit derivatives and requiring the absence of ghosts in a linearized approximation around an AdS3 background, we find that there is a unique supersymmetric invariant which we call supersymmetric ‘cubic extended’ New Massive Gravity. The purely gravitational part of this invariant is in agreement with an earlier analysis based upon the holographic c-theorem and coincides with an expansion of Born-Infeld gravity to the required order.

Our results lead us to propose an expression for the bosonic part of off-shell \( \mathcal{N} \) = 1 Born-Infeld supergravity in three dimensions that is free of ghosts. We show that different truncations of a perturbative expansion of this expression gives rise to the bosonic part of (i) Einstein supergravity; (ii) supersymmetric New Massive Gravity and (iii) supersymmetric ‘cubic extended’ New Massive Gravity.


Classical Theories of Gravity Supergravity Models 


  1. [1]
    G. Lopes Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black hole entropy, Phys. Lett. B 451 (1999) 309 [hep-th/9812082] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  4. [4]
    E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive Gravity in Three Dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  5. [5]
    S. Deser, R. Jackiw and S. Templeton, Topologically Massive Gauge Theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [INSPIRE].
  6. [6]
    I. Gullu, T.C. Sisman and B. Tekin, Born-Infeld extension of new massive gravity, Class. Quant. Grav. 27 (2010) 162001 [arXiv:1003.3935] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  7. [7]
    S. Deser and G.W. Gibbons, Born-Infeld-Einstein actions?, Class. Quant. Grav. 15 (1998) L35 [hep-th/9803049] [INSPIRE].ADSCrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    A. Sinha, On the new massive gravity and AdS/CFT, JHEP 06 (2010) 061 [arXiv:1003.0683] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    M.F. Paulos, New massive gravity extended with an arbitrary number of curvature corrections, Phys. Rev. D 82 (2010) 084042 [arXiv:1005.1646] [INSPIRE].ADSGoogle Scholar
  10. [10]
    R. Andringa, E.A. Bergshoeff, M. de Roo, O. Hohm, E. Sezgin et al., Massive 3D Supergravity, Class. Quant. Grav. 27 (2010) 025010 [arXiv:0907.4658] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    E.A. Bergshoeff, O. Hohm, J. Rosseel, E. Sezgin and P.K. Townsend, More on Massive 3D Supergravity, Class. Quant. Grav. 28 (2011) 015002 [arXiv:1005.3952] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  12. [12]
    T. Nutma, Polycritical Gravities, Phys. Rev. D 85 (2012) 124040 [arXiv:1203.5338] [INSPIRE].ADSGoogle Scholar
  13. [13]
    S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, hep-th/0108200 [INSPIRE].
  14. [14]
    P. van Nieuwenhuizen, D = 3 Conformal Supergravity and Chern-Simons Terms, Phys. Rev. D 32 (1985) 872 [INSPIRE].ADSMathSciNetGoogle Scholar
  15. [15]
    T. Uematsu, Structure of N = 1 Conformal and Poincaré Supergravity in (1 + 1)-dimensions and (2 + 1)-dimensions, Z. Phys. C 29 (1985) 143 [INSPIRE].ADSMathSciNetGoogle Scholar
  16. [16]
    T. Uematsu, Constraints and Actions in Two-dimensional and Three-dimensional N = 1 Conformal Supergravity, Z. Phys. C 32 (1986) 33 [INSPIRE].ADSMathSciNetGoogle Scholar
  17. [17]
    P.S. Howe and R.W. Tucker, Local Supersymmetry in (2 + 1)-Dimensions. 1. Supergravity and Differential Forms, J. Math. Phys. 19 (1978) 869 [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    I. Gullu, T.C. Sisman and B. Tekin, c-functions in the Born-Infeld extended New Massive Gravity, Phys. Rev. D 82 (2010) 024032 [arXiv:1005.3214] [INSPIRE].ADSGoogle Scholar
  19. [19]
    E.A. Bergshoeff, S. de Haan, W. Merbis, J. Rosseel and T. Zojer, On Three-Dimensional Tricritical Gravity, Phys. Rev. D 86 (2012) 064037 [arXiv:1206.3089] [INSPIRE].ADSGoogle Scholar
  20. [20]
    L. Apolo and M. Porrati, Nonlinear Dynamics of Parity-Even Tricritical Gravity in Three and Four Dimensions, JHEP 08 (2012) 051 [arXiv:1206.5231] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  21. [21]
    H.R. Afshar, E.A. Bergshoeff and W. Merbis, Extended massive gravity in three dimensions, arXiv:1405.6213 [INSPIRE].
  22. [22]
    D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].ADSGoogle Scholar
  23. [23]
    O. Hohm, A. Routh, P.K. Townsend and B. Zhang, On the Hamiltonian form of 3D massive gravity, Phys. Rev. D 86 (2012) 084035 [arXiv:1208.0038] [INSPIRE].ADSGoogle Scholar
  24. [24]
    E.A. Bergshoeff, O. Hohm, W. Merbis, A.J. Routh and P.K. Townsend, The Hamiltonian Form of Three-Dimensional Chern-Simons-like Gravity Models, arXiv:1402.1688 [INSPIRE].
  25. [25]
    S.J. Gates Jr. and S.V. Ketov, 4-D, N = 1 Born-Infeld supergravity, Class. Quant. Grav. 18 (2001) 3561 [hep-th/0104223] [INSPIRE].ADSCrossRefMATHMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Institute for Particle Physics and GravityUniversity of GroningenGroningenThe Netherlands

Personalised recommendations