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3D Born-Infeld gravity and supersymmetry

  • Eric Bergshoeff
  • Mehmet Ozkan
Open Access
Article

Abstract

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.

Keywords

Classical Theories of Gravity Supergravity Models 

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]
    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].CrossRefzbMATHMathSciNetGoogle 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].ADSCrossRefzbMATHMathSciNetGoogle 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].ADSCrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

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

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