Download PDF

Journal of High Energy Physics

, 2017:89 | Cite as

Three-form multiplet and supersymmetry breaking

Open Access
Regular Article - Theoretical Physics
First Online:
Received:
Revised:
Accepted:

Abstract

Recently, a nilpotent real scalar superfield V was introduced in [1] as a model for the Goldstino. It contains only two independent component fields, the Goldstino and the auxiliary D-field. Here we first show that V can equivalently be realised as a constrained three-form superfield. We demonstrate that every irreducible Goldstino superfield (of which the Goldstino is the only independent component field) can be realised as a descendant of V which is invariant under local rescalings V → e τ V, where τ is an arbitrary real scalar superfield. We next propose a new Goldstino supermultiplet which is described by a nilpotent three-form superfield \( \mathcal{Y} \) that is a variant formulation for the nilpotent chiral superfield, which is often used in off-shell models for spontaneously broken supergravity. It is shown that the action describing the dynamics of \( \mathcal{Y} \) may be obtained from a super-symmetric nonlinear σ-model in the infrared limit. Unlike V , the Goldstino superfield \( \mathcal{Y} \) contains two independent auxiliary fields, F = H + iG, of which H is a scalar and G is the field strength of a gauge three-form. When \( \mathcal{Y} \) is coupled to supergravity, both H and G produce positive contributions to the cosmological constant. While the contribution from H is uniquely determined by the parameter of the supersymmetry breaking in the action, the contribution from G is dynamical.

Keywords

Superspaces Supersymmetry Breaking 
Download to read the full article text

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]
    S.M. Kuzenko, I.N. McArthur and G. Tartaglino-Mazzucchelli, Goldstino superfields in \( \mathcal{N} \) = 2 supergravity, JHEP 05 (2017) 061 [arXiv:1702.02423] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    I. Bandos, M. Heller, S.M. Kuzenko, L. Martucci and D. Sorokin, The Goldstino brane, the constrained superfields and matter in \( \mathcal{N} \) = 1 supergravity, JHEP 11 (2016) 109 [arXiv:1608.05908] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    U. Lindström and M. Roček, Constrained local superfields, Phys. Rev. D 19 (1979) 2300 [INSPIRE].ADSGoogle Scholar
  4. [4]
    M. Roček, Linearizing the Volkov-Akulov model, Phys. Rev. Lett. 41 (1978) 451 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    E.A. Ivanov and A.A. Kapustnikov, General relationship between linear and nonlinear realizations of supersymmetry, J. Phys. A 11 (1978) 2375 [INSPIRE].ADSGoogle Scholar
  6. [6]
    S.M. Kuzenko and S.J. Tyler, Complex linear superfield as a model for Goldstino, JHEP 04 (2011) 057 [arXiv:1102.3042] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    P. Fayet and J. Iliopoulos, Spontaneously broken supergauge symmetries and Goldstone spinors, Phys. Lett. 51B (1974) 461 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    E. Dudas, S. Ferrara, A. Kehagias and A. Sagnotti, Properties of nilpotent supergravity, JHEP 09 (2015) 217 [arXiv:1507.07842] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    E.A. Bergshoeff, D.Z. Freedman, R. Kallosh and A. Van Proeyen, Pure de Sitter supergravity, Phys. Rev. D 92 (2015) 085040 [arXiv:1507.08264] [INSPIRE].ADSMathSciNetGoogle Scholar
  10. [10]
    F. Hasegawa and Y. Yamada, Component action of nilpotent multiplet coupled to matter in 4 dimensional \( \mathcal{N} \) = 1 supergravity, JHEP 10 (2015) 106 [arXiv:1507.08619] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    S.M. Kuzenko, Complex linear Goldstino superfield and supergravity, JHEP 10 (2015) 006 [arXiv:1508.03190] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    P.K. Townsend, Cosmological constant in supergravity, Phys. Rev. D 15 (1977) 2802 [INSPIRE].ADSGoogle Scholar
  13. [13]
    I. Bandos, L. Martucci, D. Sorokin and M. Tonin, Brane induced supersymmetry breaking and de Sitter supergravity, JHEP 02 (2016) 080 [arXiv:1511.03024] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    D.V. Volkov and V.A. Soroka, Higgs effect for Goldstone particles with spin 1/2, JETP Lett. 18 (1973) 312 [Pisma Zh. Eksp. Teor. Fiz. 18 (1973) 529] [INSPIRE].
  15. [15]
    D.V. Volkov and V.A. Soroka, Gauge fields for symmetry group with spinor parameters, Theor. Math. Phys. 20 (1974) 829 [INSPIRE].MathSciNetCrossRefGoogle Scholar
  16. [16]
    S. Deser and B. Zumino, Broken supersymmetry and supergravity, Phys. Rev. Lett. 38 (1977) 1433 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    R. Casalbuoni, S. De Curtis, D. Dominici, F. Feruglio and R. Gatto, Nonlinear realization of supersymmetry algebra from supersymmetric constraint, Phys. Lett. B 220 (1989) 569 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    Z. Komargodski and N. Seiberg, From linear SUSY to constrained superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    S.J. Gates, Jr., Super p form gauge superfields, Nucl. Phys. B 184 (1981) 381 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    S.J. Gates, Jr. and W. Siegel, Variant superfield representations, Nucl. Phys. B 187 (1981) 389 [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace or one thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].MATHGoogle Scholar
  22. [22]
    I.A. Batalin and G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators, Phys. Rev. D 28 (1983) 2567 [Erratum ibid. D 30 (1984) 508] [INSPIRE].
  23. [23]
    I.L. Buchbinder and S.M. Kuzenko, Quantization of the classically equivalent theories in the superspace of simple supergravity and quantum equivalence, Nucl. Phys. B 308 (1988) 162 [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    I.L. Buchbinder and S.M. Kuzenko, Ideas and methods of supersymmetry and supergravity or a walk through superspace, IOP, Bristol, U.K. (1995), revised edition (1998).Google Scholar
  25. [25]
    D.V. Volkov and V.P. Akulov, Possible universal neutrino interaction, JETP Lett. 16 (1972) 438 [Pisma Zh. Eksp. Teor. Fiz. 16 (1972) 621] [INSPIRE].
  26. [26]
    D.V. Volkov and V.P. Akulov, Is the neutrino a Goldstone particle?, Phys. Lett. 46B (1973) 109 [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    V.P. Akulov and D.V. Volkov, Goldstone fields with spin 1/2, Theor. Math. Phys. 18 (1974) 28 [Teor. Mat. Fiz. 18 (1974) 39] [INSPIRE].
  28. [28]
    S.M. Kuzenko and S.J. Tyler, On the Goldstino actions and their symmetries, JHEP 05 (2011) 055 [arXiv:1102.3043] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  29. [29]
    S.M. Kuzenko and I.N. McArthur, Goldstino superfields for spontaneously broken N = 2 supersymmetry, JHEP 06 (2011) 133 [arXiv:1105.3001] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  30. [30]
    M.J. Duncan and L.G. Jensen, Four forms and the vanishing of the cosmological constant, Nucl. Phys. B 336 (1990) 100 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    K. Groh, J. Louis and J. Sommerfeld, Duality and couplings of 3-form-multiplets in N = 1 supersymmetry, JHEP 05 (2013) 001 [arXiv:1212.4639] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    W. Siegel, A polynomial action for a massive, self-interacting chiral superfield coupled to supergravity, HUTP-77/A077 (1977).Google Scholar
  33. [33]
    M. Kaku and P.K. Townsend, Poincaré supergravity as broken superconformal gravity, Phys. Lett. 76B (1978) 54 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    S. Ferrara, L. Girardello, T. Kugo and A. Van Proeyen, Relation between different auxiliary field formulations of N = 1 supergravity coupled to Matter, Nucl. Phys. B 223 (1983) 191 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    R. Grimm, J. Wess and B. Zumino, Consistency checks on the superspace formulation of supergravity, Phys. Lett. 73B (1978) 415 [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    R. Grimm, J. Wess and B. Zumino, A complete solution of the Bianchi identities in superspace, Nucl. Phys. B 152 (1979) 255 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    J. Wess and B. Zumino, Superfield lagrangian for supergravity, Phys. Lett. 74B (1978) 51 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    K.S. Stelle and P.C. West, Minimal auxiliary fields for supergravity, Phys. Lett. 74B (1978) 330 [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    S. Ferrara and P. van Nieuwenhuizen, The auxiliary fields of supergravity, Phys. Lett. 74B (1978) 333 [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    P.S. Howe and R.W. Tucker, Scale invariance in superspace, Phys. Lett. 80B (1978) 138 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    T. Kugo and S. Uehara, Improved superconformal gauge conditions in the N = 1 supergravity Yang-Mills matter system, Nucl. Phys. B 222 (1983) 125 [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    S. Ferrara and P. van Nieuwenhuizen, Tensor calculus for supergravity, Phys. Lett. B 76 (1978) 404.ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    W. Siegel, Solution to constraints in Wess-Zumino supergravity formalism, Nucl. Phys. B 142 (1978) 301 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    D. Butter and S.M. Kuzenko, A dual formulation of supergravity-matter theories, Nucl. Phys. B 854 (2012) 1 [arXiv:1106.3038] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  45. [45]
    M.F. Sohnius and P.C. West, An alternative minimal off-shell version of N = 1 supergravity, Phys. Lett. 105B (1981) 353 [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    M.F. Sohnius and P.C. West, The new minimal formulation of N = 1 supergravity and its tensor calculus, in Quantum structure of space and Time, M.J. Duff and C.J. Isham eds., Cambridge University Press, Cambridge U.K. (1982).Google Scholar
  47. [47]
    M. Sohnius and P.C. West, The tensor calculus and matter coupling of the alternative minimal auxiliary field formulation of N = 1 supergravity, Nucl. Phys. B 198 (1982) 493 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    W. Siegel and S.J. Gates Jr., Superfield supergravity, Nucl. Phys. B 147 (1979) 77 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  49. [49]
    P. Binetruy, F. Pillon, G. Girardi and R. Grimm, The three form multiplet in supergravity, Nucl. Phys. B 477 (1996) 175 [hep-th/9603181] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  50. [50]
    B.A. Ovrut and D. Waldram, Membranes and three form supergravity, Nucl. Phys. B 506 (1997) 236 [hep-th/9704045] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  51. [51]
    S.M. Kuzenko and S.A. McCarthy, On the component structure of N = 1 supersymmetric nonlinear electrodynamics, JHEP 05 (2005) 012 [hep-th/0501172] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  52. [52]
    I.A. Bandos and C. Meliveo, Supermembrane interaction with dynamical D = 4 N = 1 supergravity. Superfield Lagrangian description and spacetime equations of motion, JHEP 08 (2012) 140 [arXiv:1205.5885] [INSPIRE].
  53. [53]
    V. Ogievetsky and E. Sokatchev, Equation of motion for the axial gravitational superfield, Sov. J. Nucl. Phys. 32 (1980) 589 [Yad. Fiz. 32 (1980) 1142] [INSPIRE].
  54. [54]
    M.J. Duff and P. van Nieuwenhuizen, Quantum inequivalence of different field representations, Phys. Lett. B 94 (1980) 179.ADSCrossRefGoogle Scholar
  55. [55]
    A. Aurilia, H. Nicolai and P.K. Townsend, Hidden constants: the theta parameter of QCD and the cosmological constant of N = 8 supergravity, Nucl. Phys. B 176 (1980) 509 [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    S.W. Hawking, The cosmological constant is probably zero, Phys. Lett. B 134 (1984) 403.ADSCrossRefGoogle Scholar
  57. [57]
    M.J. Duff, The cosmological constant is possibly zero, but the proof is probably wrong, Phys. Lett. B 226 (1989) 36 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  58. [58]
    R. Bousso and J. Polchinski, Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  59. [59]
    F. Farakos, A. Kehagias, D. Racco and A. Riotto, Scanning of the supersymmetry breaking scale and the gravitino mass in supergravity, JHEP 06 (2016) 120 [arXiv:1605.07631] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.School of Physics and Astrophysics M013The University of Western AustraliaCrawleyAustralia

Personalised recommendations