Advertisement

Ghostbusters in f (R) supergravity

  • Toshiaki Fujimori
  • Muneto Nitta
  • Keisuke Ohashi
  • Yusuke Yamada
Open Access
Regular Article - Theoretical Physics
  • 37 Downloads

Abstract

f (R) supergravity is known to contain a ghost mode associated with higher-derivative terms if it contains R n with n greater than two. We remove the ghost in f (R) supergravity by introducing auxiliary gauge field to absorb the ghost. We dub this method as the ghostbuster mechanism [1]. We show that the mechanism removes the ghost super-multiplet but also terms including R n with n ≥ 3, after integrating out auxiliary degrees of freedom. For pure supergravity case, there appears an instability in the resultant scalar potential. We then show that the instability of the scalar potential can be cured by introducing matter couplings in such a way that the system has a stable potential.

Keywords

Supergravity Models Supersymmetric Effective Theories 

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]
    T. Fujimori, M. Nitta and Y. Yamada, Ghostbusters in higher derivative supersymmetric theories: who is afraid of propagating auxiliary fields?, JHEP 09 (2016) 106 [arXiv:1608.01843] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    M. Ostrogradski, Mémoires sur les équations différentielles, relatives au problème des isopérimètres (in French), Mem. Ac. St. Petersbourg 6 (1850) 385 [INSPIRE].
  3. [3]
    R.P. Woodard, Avoiding dark energy with 1/r modifications of gravity, Lect. Notes Phys. 720 (2007) 403 [astro-ph/0601672] [INSPIRE].
  4. [4]
    G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].MathSciNetCrossRefGoogle Scholar
  5. [5]
    T. Kobayashi, M. Yamaguchi and J. Yokoyama, Generalized G-inflation: inflation with the most general second-order field equations, Prog. Theor. Phys. 126 (2011) 511 [arXiv:1105.5723] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  6. [6]
    A. Nicolis, R. Rattazzi and E. Trincherini, The galileon as a local modification of gravity, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197] [INSPIRE].
  7. [7]
    F. Farakos, C. Germani and A. Kehagias, On ghost-free supersymmetric galileons, JHEP 11 (2013) 045 [arXiv:1306.2961] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    D. Roest, P. Werkman and Y. Yamada, Internal supersymmetry and small-field goldstini, arXiv:1710.02480 [INSPIRE].
  9. [9]
    A.A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  10. [10]
    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20 [arXiv:1502.02114] [INSPIRE].
  11. [11]
    H.A. Buchdahl, Non-linear Lagrangians and cosmological theory, Mon. Not. Roy. Astron. Soc. 150 (1970) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    A. De Felice and S. Tsujikawa, f (R) theories, Living Rev. Rel. 13 (2010) 3 [arXiv:1002.4928] [INSPIRE].
  13. [13]
    S. Nojiri, S.D. Odintsov and V.K. Oikonomou, Modified gravity theories on a nutshell: inflation, bounce and late-time evolution, Phys. Rept. 692 (2017) 1 [arXiv:1705.11098] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    S.J. Gates Jr., Why auxiliary fields matter: the strange case of the 4D, N = 1 supersymmetric QCD effective action, Phys. Lett. B 365 (1996) 132 [hep-th/9508153] [INSPIRE].
  15. [15]
    S.J. Gates Jr., Why auxiliary fields matter: the strange case of the 4D, N = 1 supersymmetric QCD effective action. 2, Nucl. Phys. B 485 (1997) 145 [hep-th/9606109] [INSPIRE].
  16. [16]
    I. Antoniadis, E. Dudas and D.M. Ghilencea, Supersymmetric models with higher dimensional operators, JHEP 03 (2008) 045 [arXiv:0708.0383] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    E. Dudas and D.M. Ghilencea, Effective operators in SUSY, superfield constraints and searches for a UV completion, JHEP 06 (2015) 124 [arXiv:1503.08319] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    J. Khoury, J.-L. Lehners and B. Ovrut, Supersymmetric P(X, \( \phi \)) and the ghost condensate, Phys. Rev. D 83 (2011) 125031 [arXiv:1012.3748] [INSPIRE].
  19. [19]
    J. Khoury, J.-L. Lehners and B.A. Ovrut, Supersymmetric galileons, Phys. Rev. D 84 (2011) 043521 [arXiv:1103.0003] [INSPIRE].
  20. [20]
    M. Koehn, J.-L. Lehners and B.A. Ovrut, Higher-derivative chiral superfield actions coupled to N = 1 supergravity, Phys. Rev. D 86 (2012) 085019 [arXiv:1207.3798] [INSPIRE].
  21. [21]
    M. Koehn, J.-L. Lehners and B. Ovrut, Ghost condensate in N = 1 supergravity, Phys. Rev. D 87 (2013) 065022 [arXiv:1212.2185] [INSPIRE].
  22. [22]
    T. Fujimori, M. Nitta, K. Ohashi, Y. Yamada and R. Yokokura, Ghost-free vector superfield actions in supersymmetric higher-derivative theories, JHEP 09 (2017) 143 [arXiv:1708.05129] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    I.L. Buchbinder, S. Kuzenko and Z. Yarevskaya, Supersymmetric effective potential: superfield approach, Nucl. Phys. B 411 (1994) 665 [INSPIRE].
  24. [24]
    I.L. Buchbinder, S.M. Kuzenko and A. Yu. Petrov, Superfield chiral effective potential, Phys. Lett. B 321 (1994) 372 [INSPIRE].
  25. [25]
    A.T. Banin, I.L. Buchbinder and N.G. Pletnev, On quantum properties of the four-dimensional generic chiral superfield model, Phys. Rev. D 74 (2006) 045010 [hep-th/0606242] [INSPIRE].
  26. [26]
    S.M. Kuzenko and S.J. Tyler, The one-loop effective potential of the Wess-Zumino model revisited, JHEP 09 (2014) 135 [arXiv:1407.5270] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    M. Nitta and S. Sasaki, Higher derivative corrections to manifestly supersymmetric nonlinear realizations, Phys. Rev. D 90 (2014) 105002 [arXiv:1408.4210] [INSPIRE].ADSGoogle Scholar
  28. [28]
    F. Farakos and A. Kehagias, Emerging potentials in higher-derivative gauged chiral models coupled to N = 1 supergravity, JHEP 11 (2012) 077 [arXiv:1207.4767] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    S. Sasaki, M. Yamaguchi and D. Yokoyama, Supersymmetric DBI inflation, Phys. Lett. B 718 (2012) 1 [arXiv:1205.1353] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    S. Aoki and Y. Yamada, Inflation in supergravity without Kähler potential, Phys. Rev. D 90 (2014) 127701 [arXiv:1409.4183] [INSPIRE].
  31. [31]
    S. Aoki and Y. Yamada, Impacts of supersymmetric higher derivative terms on inflation models in supergravity, JCAP 07 (2015) 020 [arXiv:1504.07023] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, Extended supersymmetry and BPS solutions in baby Skyrme models, JHEP 05 (2013) 108 [arXiv:1304.0774] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, N = 1 supersymmetric extension of the baby Skyrme model, Phys. Rev. D 84 (2011) 025008 [arXiv:1105.1168] [INSPIRE].
  34. [34]
    M. Nitta and S. Sasaki, BPS states in supersymmetric chiral models with higher derivative terms, Phys. Rev. D 90 (2014) 105001 [arXiv:1406.7647] [INSPIRE].ADSGoogle Scholar
  35. [35]
    M. Nitta and S. Sasaki, Classifying BPS states in supersymmetric gauge theories coupled to higher derivative chiral models, Phys. Rev. D 91 (2015) 125025 [arXiv:1504.08123] [INSPIRE].ADSMathSciNetGoogle Scholar
  36. [36]
    S. Bolognesi and W. Zakrzewski, Baby Skyrme model, near-BPS approximations and supersymmetric extensions, Phys. Rev. D 91 (2015) 045034 [arXiv:1407.3140] [INSPIRE].
  37. [37]
    J.M. Queiruga, Baby Skyrme model and fermionic zero modes, Phys. Rev. D 94 (2016) 065022 [arXiv:1606.02869] [INSPIRE].
  38. [38]
    S.B. Gudnason, M. Nitta and S. Sasaki, A supersymmetric Skyrme model, JHEP 02 (2016) 074 [arXiv:1512.07557] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    S.B. Gudnason, M. Nitta and S. Sasaki, Topological solitons in the supersymmetric Skyrme model, JHEP 01 (2017) 014 [arXiv:1608.03526] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    J.M. Queiruga, Skyrme-like models and supersymmetry in 3 + 1 dimensions, Phys. Rev. D 92 (2015) 105012 [arXiv:1508.06692] [INSPIRE].
  41. [41]
    J.M. Queiruga and A. Wereszczynski, Non-uniqueness of the supersymmetric extension of the O(3) σ-model, JHEP 11 (2017) 141 [arXiv:1703.07343] [INSPIRE].
  42. [42]
    M. Eto, T. Fujimori, M. Nitta, K. Ohashi and N. Sakai, Higher derivative corrections to non-Abelian vortex effective theory, Prog. Theor. Phys. 128 (2012) 67 [arXiv:1204.0773] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  43. [43]
    M. Nitta, S. Sasaki and R. Yokokura, Spatially modulated vacua in relativistic field theories, arXiv:1706.02938 [INSPIRE].
  44. [44]
    M. Nitta, S. Sasaki and R. Yokokura, Supersymmetry breaking in spatially modulated vacua, Phys. Rev. D 96 (2017) 105022 [arXiv:1706.05232] [INSPIRE].
  45. [45]
    S. Cecotti and S. Ferrara, Supersymmetric Born-Infeld lagrangians, Phys. Lett. B 187 (1987) 335 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  46. [46]
    J. Bagger and A. Galperin, A new Goldstone multiplet for partially broken supersymmetry, Phys. Rev. D 55 (1997) 1091 [hep-th/9608177] [INSPIRE].ADSMathSciNetGoogle Scholar
  47. [47]
    M. Roček and A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields and three-brane actions, Phys. Rev. D 59 (1999) 106001 [hep-th/9811232] [INSPIRE].
  48. [48]
    S.M. Kuzenko and S.A. McCarthy, Nonlinear selfduality and supergravity, JHEP 02 (2003) 038 [hep-th/0212039] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    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].
  50. [50]
    H. Abe, Y. Sakamura and Y. Yamada, Matter coupled Dirac-Born-Infeld action in four-dimensional N = 1 conformal supergravity, Phys. Rev. D 92 (2015) 025017 [arXiv:1504.01221] [INSPIRE].
  51. [51]
    S. Cecotti, S. Ferrara and L. Girardello, Structure of the scalar potential in general N = 1 higher derivative supergravity in four-dimensions, Phys. Lett. B 187 (1987) 321 [INSPIRE].
  52. [52]
    F. Farakos, S. Ferrara, A. Kehagias and M. Porrati, Supersymmetry breaking by higher dimension operators, Nucl. Phys. B 879 (2014) 348 [arXiv:1309.1476] [INSPIRE].
  53. [53]
    S.M. Kuzenko and S. Theisen, Supersymmetric duality rotations, JHEP 03 (2000) 034 [hep-th/0001068] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    S.M. Kuzenko and S. Theisen, Nonlinear selfduality and supersymmetry, Fortsch. Phys. 49 (2001) 273 [hep-th/0007231] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  55. [55]
    S.M. Kuzenko, The Fayet-Iliopoulos term and nonlinear self-duality, Phys. Rev. D 81 (2010) 085036 [arXiv:0911.5190] [INSPIRE].
  56. [56]
    S. Cecotti, Higher derivative supergravity is equivalent to standard supergravity coupled to matter. 1, Phys. Lett. B 190 (1987) 86 [INSPIRE].
  57. [57]
    S. Ferrara, A. Kehagias and A. Riotto, The imaginary Starobinsky model and higher curvature corrections, Fortsch. Phys. 63 (2015) 2 [arXiv:1405.2353] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  58. [58]
    F. Farakos, S. Ferrara, A. Kehagias and D. Lüst, Non-linear realizations and higher curvature supergravity, Fortsch. Phys. 65 (2017) 1700073 [arXiv:1707.06991] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  59. [59]
    G.A. Diamandis, B.C. Georgalas, K. Kaskavelis, A.B. Lahanas and G. Pavlopoulos, Deforming the Starobinsky model in ghost-free higher derivative supergravities, Phys. Rev. D 96 (2017) 044033 [arXiv:1704.07617] [INSPIRE].
  60. [60]
    D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K., (2012) [INSPIRE].
  61. [61]
    R. Kallosh and A. Linde, Superconformal generalizations of the Starobinsky model, JCAP 06 (2013) 028 [arXiv:1306.3214] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  62. [62]
    F. Farakos, A. Kehagias and A. Riotto, On the Starobinsky model of inflation from supergravity, Nucl. Phys. B 876 (2013) 187 [arXiv:1307.1137] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  63. [63]
    S.V. Ketov and T. Terada, Old-minimal supergravity models of inflation, JHEP 12 (2013) 040 [arXiv:1309.7494] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  64. [64]
    M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Properties of conformal supergravity, Phys. Rev. D 17 (1978) 3179 [INSPIRE].ADSMathSciNetGoogle Scholar
  65. [65]
    M. Kaku and P.K. Townsend, Poincaré supergravity as broken superconformal gravity, Phys. Lett. B 76 (1978) 54 [INSPIRE].
  66. [66]
    P.K. Townsend and P. van Nieuwenhuizen, Simplifications of conformal supergravity, Phys. Rev. D 19 (1979) 3166 [INSPIRE].ADSMathSciNetGoogle Scholar
  67. [67]
    T. Kugo and S. Uehara, Conformal and Poincaré tensor calculi in N = 1 supergravity, Nucl. Phys. B 226 (1983) 49 [INSPIRE].
  68. [68]
    M. Ozkan and Y. Pang, R n extension of Starobinsky model in old minimal supergravity, Class. Quant. Grav. 31 (2014) 205004 [arXiv:1402.5427] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  69. [69]
    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].
  70. [70]
    S. Cecotti and R. Kallosh, Cosmological attractor models and higher curvature supergravity, JHEP 05 (2014) 114 [arXiv:1403.2932] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  71. [71]
    R. Kallosh, A. Linde and D. Roest, Superconformal inflationary α-attractors, JHEP 11 (2013) 198 [arXiv:1311.0472] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  72. [72]
    J.J.M. Carrasco, R. Kallosh, A. Linde and D. Roest, Hyperbolic geometry of cosmological attractors, Phys. Rev. D 92 (2015) 041301 [arXiv:1504.05557] [INSPIRE].
  73. [73]
    M.F. Sohnius and P.C. West, An alternative minimal off-shell version of N = 1 supergravity, Phys. Lett. B 105 (1981) 353 [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Physics & Research and Education Center for Natural SciencesKeio UniversityYokohamaJapan
  2. 2.Stanford Institute for Theoretical Physics and Department of PhysicsStanford UniversityStanfordU.S.A.

Personalised recommendations