Advertisement

Critical \( \mathcal{N} \) = (1, 1) general massive supergravity

  • Nihat Sadik Deger
  • George Moutsopoulos
  • Jan Rosseel
Open Access
Regular Article - Theoretical Physics

Abstract

In this paper we study the supermultiplet structure of \( \mathcal{N} \) = (1, 1) General Massive Supergravity at non-critical and critical points of its parameter space. To do this, we first linearize the theory around its maximally supersymmetric AdS3 vacuum and obtain the full linearized Lagrangian including fermionic terms. At generic values, linearized modes can be organized as two massless and 2 massive multiplets where supersymmetry relates them in the standard way. At critical points logarithmic modes appear and we find that in three of such points some of the supersymmetry transformations are non-invertible in logarithmic multiplets. However, in the fourth critical point, there is a massive logarithmic multiplet with invertible supersymmetry transformations.

Keywords

Supergravity Models AdS-CFT Correspondence 

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]
    V. Gurarie, Logarithmic operators in conformal field theory, Nucl. Phys. B 410 (1993) 535 [hep-th/9303160] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    M.A.I. Flohr, Two-dimensional turbulence: yet another conformal field theory solution, Nucl. Phys. B 482 (1996) 567 [hep-th/9606130] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  3. [3]
    D. Grumiller, W. Riedler, J. Rosseel and T. Zojer, Holographic applications of logarithmic conformal field theories, J. Phys. A 46 (2013) 494002 [arXiv:1302.0280] [INSPIRE].MathSciNetMATHGoogle Scholar
  4. [4]
    D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point, JHEP 07 (2008) 134 [arXiv:0805.2610] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  5. [5]
    E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive gravity in three dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    E.A. Bergshoeff, O. Hohm and P.K. Townsend, More on massive 3D gravity, Phys. Rev. D 79 (2009) 124042 [arXiv:0905.1259] [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    H. Lü and C.N. Pope, Critical gravity in four dimensions, Phys. Rev. Lett. 106 (2011) 181302 [arXiv:1101.1971] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S. Deser et al., Critical points of D-dimensional extended gravities, Phys. Rev. D 83 (2011) 061502 [arXiv:1101.4009] [INSPIRE].ADSGoogle Scholar
  9. [9]
    E.A. Bergshoeff, O. Hohm, J. Rosseel and P.K. Townsend, Modes of log gravity, Phys. Rev. D 83 (2011) 104038 [arXiv:1102.4091] [INSPIRE].ADSGoogle Scholar
  10. [10]
    I.L. Buchbinder et al., New 4D, N = 1 superfield theory: Model of free massive superspin 3/2 multiplet, Phys. Lett. B 535 (2002) 280 [hep-th/0201096] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    T. Gregoire, M.D. Schwartz and Y. Shadmi, Massive supergravity and deconstruction, JHEP 07 (2004) 029 [hep-th/0403224] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    I.L. Buchbinder, S. James Gates, Jr., S.M. Kuzenko and J. Phillips, Massive 4D, N = 1 superspin 1&3/2 multiplets and dualities, JHEP 02 (2005) 056 [hep-th/0501199] [INSPIRE].
  13. [13]
    S.J. Gates Jr., S.M. Kuzenko and G. Tartaglino-Mazzucchelli, New massive supergravity multiplets, JHEP 02 (2007) 052 [hep-th/0610333] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    S.J. Gates Jr. and K. Koutrolikos, A dynamical theory for linearized massive superspin 3/2, JHEP 03 (2014) 030 [arXiv:1310.7387] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    H. Lü, C.N. Pope, E. Sezgin and L. Wulff, Critical and non-critical Einstein-Weyl supergravity, JHEP 10 (2011) 131 [arXiv:1107.2480] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    S. Deser and J.H. Kay, Topologically massive supergravity, Phys. Lett. B 120 (1983) 97 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    R. Andringa et al., Massive 3D supergravity, Class. Quant. Grav. 27 (2010) 025010 [arXiv:0907.4658] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    E.A. Bergshoeff et al., On critical massive (super)gravity in AdS 3, J. Phys. Conf. Ser. 314 (2011) 012009 [arXiv:1011.1153] [INSPIRE].CrossRefGoogle Scholar
  20. [20]
    G. Alkaç et al., Massive \( \mathcal{N} \) = 2 supergravity in three dimensions, JHEP 02 (2015) 125 [arXiv:1412.3118] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Three-dimensional N = 2 (AdS) supergravity and associated supercurrents, JHEP 12 (2011) 052 [arXiv:1109.0496] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    S.M. Kuzenko et al., Three-dimensional \( \mathcal{N} \) = 2 supergravity theories: From superspace to components, Phys. Rev. D 89 (2014) 085028 [arXiv:1312.4267] [INSPIRE].ADSGoogle Scholar
  23. [23]
    S.M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, Higher derivative couplings and massive supergravity in three dimensions, JHEP 09 (2015) 081 [arXiv:1506.09063] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  24. [24]
    N.S. Deger, A. Kaya, H. Samtleben and E. Sezgin, Supersymmetric warped AdS in extended topologically massive supergravity, Nucl. Phys. B 884 (2014) 106 [arXiv:1311.4583] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    G. Alkac et al., Supersymmetric backgrounds and black holes in \( \mathcal{N} \) = (1, 1) cosmological new massive supergravity, JHEP 10 (2015) 141 [arXiv:1507.06928] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    N.S. Deger and G. Moutsopoulos, Supersymmetric solutions of N = (2, 0) topologically massive supergravity, Class. Quant. Grav. 33 (2016) 155006 [arXiv:1602.07263] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    M. Roček and P. van Nieuwenhuizen, N ≥ 2 supersymmetric Chern-Simons terms as d = 3 extended conformal supergravity, Class. Quant. Grav. 3 (1986) 43 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    H. Nishino and S.J. Gates, Jr., Chern-Simons theories with supersymmetries in three-dimensions, Int. J. Mod. Phys. A 8 (1993) 3371 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    E. Bergshoeff, S. Cecotti, H. Samtleben and E. Sezgin, Superconformal σ-models in three dimensions, Nucl. Phys. B 838 (2010) 266 [arXiv:1002.4411] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    M. Becker, P. Bruillard and S. Downes, Chiral supergravity, JHEP 10 (2009) 004 [arXiv:0906.4822] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    D. Grumiller and I. Sachs, AdS 3 /LCFT 2correlators in cosmological topologically massive gravity, JHEP 03 (2010) 012 [arXiv:0910.5241] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  32. [32]
    D. Grumiller and O. Hohm, AdS 3 /LCFT 2 : correlators in new massive gravity, Phys. Lett. B 686 (2010) 264 [arXiv:0911.4274] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    D. Grumiller, N. Johansson and T. Zojer, Short-cut to new anomalies in gravity duals to logarithmic conformal field theories, JHEP 01 (2011) 090 [arXiv:1010.4449] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    M. Khorrami, A. Aghamohammadi and A.M. Ghezelbash, Logarithmic N = 1 superconformal field theories, Phys. Lett. B 439 (1998) 283 [hep-th/9803071] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    D. Drichel and M. Flohr, Correlation functions in N = 3 superconformal theory, arXiv:1006.3346 [INSPIRE].
  36. [36]
    P.A. Pearce, J. Rasmussen and E. Tartaglia, Logarithmic superconformal minimal models, J. Stat. Mech. 1405 (2014) P05001 [arXiv:1312.6763] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  37. [37]
    D. Grumiller and P. van Nieuwenhuizen, Holographic counterterms from local supersymmetry without boundary conditions, Phys. Lett. B 682 (2010) 462 [arXiv:0908.3486] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Nihat Sadik Deger
    • 1
    • 2
  • George Moutsopoulos
    • 1
  • Jan Rosseel
    • 3
  1. 1.Department of MathematicsBogazici UniversityBebekTurkey
  2. 2.Feza Gursey Center for Physics and MathematicsBogazici UniversityKandilliTurkey
  3. 3.Faculty of PhysicsUniversity of ViennaViennaAustria

Personalised recommendations