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New Fayet-Iliopoulos terms in \( \mathcal{N}=2 \) supergravity

  • Ignatios Antoniadis
  • Jean-Pierre Derendinger
  • Fotis FarakosEmail author
  • Gabriele Tartaglino-Mazzucchelli
Open Access
Regular Article - Theoretical Physics

Abstract

We present a new type of Fayet-Iliopoulos (FI) terms in \( \mathcal{N}=2 \) supergravity that do not require the gauging of the R-symmetry. We elaborate on the impact of such terms on the vacuum structure of the \( \mathcal{N}=2 \) theory and compare their properties with the standard Fayet-Iliopoulos terms that arise from gaugings. In particular, we show that, with the use of the new FI terms, models with a single physical \( \mathcal{N}=2 \) vector multiplet can be constructed that give stable de Sitter vacua.

Keywords

Extended Supersymmetry Supergravity Models Superspaces Supersymmetry Breaking 

Notes

Open Access

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References

  1. [1]
    B. de Wit, P.G. Lauwers and A. Van Proeyen, Lagrangians of N = 2 supergravity-matter systems, Nucl. Phys. B 255 (1985) 569 [INSPIRE].
  2. [2]
    E. Cremmer et al., Vector Multiplets Coupled to N = 2 Supergravity: SuperHiggs Effect, Flat Potentials and Geometric Structure, Nucl. Phys. B 250 (1985) 385 [INSPIRE].
  3. [3]
    R. D’Auria, S. Ferrara and P. Fré, Special and quaternionic isometries: General couplings in N = 2 supergravity and the scalar potential, Nucl. Phys. B 359 (1991) 705 [INSPIRE].
  4. [4]
    L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara and P. Fré’, General matter coupled N = 2 supergravity, Nucl. Phys. B 476 (1996) 397 [hep-th/9603004] [INSPIRE].
  5. [5]
    L. Andrianopoli et al., N = 2 supergravity and N = 2 superYang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map, J. Geom. Phys. 23 (1997) 111 [hep-th/9605032] [INSPIRE].
  6. [6]
    G. Dall’Agata, R. D’Auria, L. Sommovigo and S. Vaula, D = 4, N = 2 gauged supergravity in the presence of tensor multiplets, Nucl. Phys. B 682 (2004) 243 [hep-th/0312210] [INSPIRE].
  7. [7]
    D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, (2012).Google Scholar
  8. [8]
    M. Trigiante, Gauged Supergravities, Phys. Rept. 680 (2017) 1 [arXiv:1609.09745] [INSPIRE].
  9. [9]
    P. Fayet and J. Iliopoulos, Spontaneously Broken Supergauge Symmetries and Goldstone Spinors, Phys. Lett. 51B (1974) 461 [INSPIRE].
  10. [10]
    P. Fayet, Fermi-Bose Hypersymmetry, Nucl. Phys. B 113 (1976) 135 [INSPIRE].
  11. [11]
    A. Van Proeyen, Supergravity with Fayet-Iliopoulos terms and R-symmetry, Fortsch. Phys. 53 (2005) 997 [hep-th/0410053] [INSPIRE].
  12. [12]
    P. Fré, M. Trigiante and A. Van Proeyen, Stable de Sitter vacua from N = 2 supergravity, Class. Quant. Grav. 19 (2002) 4167 [hep-th/0205119] [INSPIRE].
  13. [13]
    F. Catino, C.A. Scrucca and P. Smyth, Simple metastable de Sitter vacua in N = 2 gauged supergravity, JHEP 04 (2013) 056 [arXiv:1302.1754] [INSPIRE].
  14. [14]
    I. Antoniadis, E. Dudas, S. Ferrara and A. Sagnotti, The Volkov-Akulov-Starobinsky supergravity, Phys. Lett. B 733 (2014) 32 [arXiv:1403.3269] [INSPIRE].
  15. [15]
    E. Dudas, S. Ferrara, A. Kehagias and A. Sagnotti, Properties of Nilpotent Supergravity, JHEP 09 (2015) 217 [arXiv:1507.07842] [INSPIRE].
  16. [16]
    E.A. Bergshoeff, D.Z. Freedman, R. Kallosh and A. Van Proeyen, Pure de Sitter Supergravity, Phys. Rev. D 92 (2015) 085040 [Erratum ibid. D 93 (2016) 069901] [arXiv:1507.08264] [INSPIRE].
  17. [17]
    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].
  18. [18]
    S.M. Kuzenko, Complex linear Goldstino superfield and supergravity, JHEP 10 (2015) 006 [arXiv:1508.03190] [INSPIRE].
  19. [19]
    I. Antoniadis and C. Markou, The coupling of Non-linear Supersymmetry to Supergravity, Eur. Phys. J. C 75 (2015) 582 [arXiv:1508.06767] [INSPIRE].
  20. [20]
    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].
  21. [21]
    N. Cribiori, G. Dall’Agata, F. Farakos and M. Porrati, Minimal Constrained Supergravity, Phys. Lett. B 764 (2017) 228 [arXiv:1611.01490] [INSPIRE].
  22. [22]
    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].
  23. [23]
    N. Cribiori, F. Farakos, M. Tournoy and A. van Proeyen, Fayet-Iliopoulos terms in supergravity without gauged R-symmetry, JHEP 04 (2018) 032 [arXiv:1712.08601] [INSPIRE].
  24. [24]
    S.M. Kuzenko, Taking a vector supermultiplet apart: Alternative Fayet-Iliopoulos-type terms, Phys. Lett. B 781 (2018) 723 [arXiv:1801.04794] [INSPIRE].
  25. [25]
    I. Antoniadis, A. Chatrabhuti, H. Isono and R. Knoops, Fayet-Iliopoulos terms in supergravity and D-term inflation, Eur. Phys. J. C 78 (2018) 366 [arXiv:1803.03817] [INSPIRE].
  26. [26]
    I. Antoniadis, A. Chatrabhuti, H. Isono and R. Knoops, The cosmological constant in Supergravity, Eur. Phys. J. C 78 (2018) 718 [arXiv:1805.00852] [INSPIRE].
  27. [27]
    E.S. Kandelakis, Extended Akulov-Volkov Superfield Theory, Phys. Lett. B 174 (1986) 301 [INSPIRE].
  28. [28]
    S.M. Kuzenko and I.N. McArthur, Goldstino superfields for spontaneously broken N = 2 supersymmetry, JHEP 06 (2011) 133 [arXiv:1105.3001] [INSPIRE].
  29. [29]
    N. Cribiori, G. Dall’Agata and F. Farakos, Interactions of N Goldstini in Superspace, Phys. Rev. D 94 (2016) 065019 [arXiv:1607.01277] [INSPIRE].
  30. [30]
    L. Girardello and M.T. Grisaru, Soft Breaking of Supersymmetry, Nucl. Phys. B 194 (1982) 65 [INSPIRE].
  31. [31]
    J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton, U.S.A., (1992).Google Scholar
  32. [32]
    A. Karlhede, U. Lindström and M. Roček, Selfinteracting Tensor Multiplets in N = 2 Superspace, Phys. Lett. 147B (1984) 297 [INSPIRE].
  33. [33]
    U. Lindström and M. Roček, New HyperKähler Metrics and New Supermultiplets, Commun. Math. Phys. 115 (1988) 21 [INSPIRE].
  34. [34]
    U. Lindström and M. Roček, N = 2 SuperYang-Mills Theory in Projective Superspace, Commun. Math. Phys. 128 (1990) 191 [INSPIRE].
  35. [35]
    U. Lindström and M. Roček, Properties of hyperKähler manifolds and their twistor spaces, Commun. Math. Phys. 293 (2010) 257 [arXiv:0807.1366] [INSPIRE].
  36. [36]
    S.M. Kuzenko, Lectures on nonlinear sigma-models in projective superspace, J. Phys. A 43 (2010) 443001 [arXiv:1004.0880] [INSPIRE].
  37. [37]
    I. Antoniadis, H. Partouche and T.R. Taylor, Spontaneous breaking of N = 2 global supersymmetry, Phys. Lett. B 372 (1996) 83 [hep-th/9512006] [INSPIRE].
  38. [38]
    R. Grimm, M. Sohnius and J. Wess, Extended Supersymmetry and Gauge Theories, Nucl. Phys. B 133 (1978) 275 [INSPIRE].
  39. [39]
    D. Butter and J. Novak, Component reduction in N = 2 supergravity: the vector, tensor and vector-tensor multiplets, JHEP 05 (2012) 115 [arXiv:1201.5431] [INSPIRE].
  40. [40]
    I. Antoniadis, H. Jiang and O. Lacombe, \( \mathcal{N}=2 \) Supersymmetry Deformations, Electromagnetic Duality and Dirac-Born-Infeld Actions, arXiv:1904.06339 [INSPIRE].
  41. [41]
    E.A. Ivanov and B.M. Zupnik, Modified N = 2 supersymmetry and Fayet-Iliopoulos terms, Phys. Atom. Nucl. 62 (1999) 1043 [Yad. Fiz. 62 (1999) 1110] [hep-th/9710236] [INSPIRE].
  42. [42]
    E. Ivanov and B. Zupnik, Modifying N = 2 supersymmetry via partial breaking, in Theory of elementary particles. Proceedings, 31st International Symposium Ahrenshoop, Buckow, Germany, September 2-6, 1997, pp. 64-69, 1998, hep-th/9801016 [INSPIRE].
  43. [43]
    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].
  44. [44]
    S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Nilpotent chiral superfield in N = 2 supergravity and partial rigid supersymmetry breaking, JHEP 03 (2016) 092 [arXiv:1512.01964] [INSPIRE].
  45. [45]
    I. Antoniadis, J.-P. Derendinger and C. Markou, Nonlinear \( \mathcal{N}=2 \) global supersymmetry, JHEP 06 (2017) 052 [arXiv:1703.08806] [INSPIRE].
  46. [46]
    N. Cribiori and S. Lanza, On the dynamical origin of parameters in \( \mathcal{N}=2 \) supersymmetry, Eur. Phys. J. C 79 (2019) 32 [arXiv:1810.11425] [INSPIRE].
  47. [47]
    S.M. Kuzenko, Super-Weyl anomalies in N = 2 supergravity and (non)local effective actions, JHEP 10 (2013) 151 [arXiv:1307.7586] [INSPIRE].
  48. [48]
    S.M. Kuzenko and G. Tartaglino-Mazzucchelli, New nilpotent \( \mathcal{N}=2 \) superfields, Phys. Rev. D 97 (2018) 026003 [arXiv:1707.07390] [INSPIRE].
  49. [49]
    D. Butter, N = 2 Conformal Superspace in Four Dimensions, JHEP 10 (2011) 030 [arXiv:1103.5914] [INSPIRE].
  50. [50]
    B. de Wit, J.W. van Holten and A. Van Proeyen, Transformation Rules of N = 2 Supergravity Multiplets, Nucl. Phys. B 167 (1980) 186 [INSPIRE].
  51. [51]
    E. Bergshoeff, M. de Roo and B. de Wit, Extended Conformal Supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].
  52. [52]
    B. de Wit, J.W. van Holten and A. Van Proeyen, Structure of N = 2 Supergravity, Nucl. Phys. B 184 (1981) 77 [Erratum ibid. B 222 (1983) 516] [INSPIRE].
  53. [53]
    N. Cribiori and G. Dall’Agata, On the off-shell formulation of N = 2 supergravity with tensor multiplets, JHEP 08 (2018) 132 [arXiv:1803.08059] [INSPIRE].
  54. [54]
    I.L. Buchbinder and S.M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity, Or a Walk Through Superspace, IOP, Bristol, U.S.A., (1998).Google Scholar
  55. [55]
    L. Baulieu, M.P. Bellon and R. Grimm, BRS Symmetry of Supergravity in Superspace and Its Projection to Component Formalism, Nucl. Phys. B 294 (1987) 279 [INSPIRE].
  56. [56]
    P. Binetruy, G. Girardi and R. Grimm, Supergravity couplings: A geometric formulation, Phys. Rept. 343 (2001) 255 [hep-th/0005225] [INSPIRE].
  57. [57]
    J. Wess, Supersymmetry and Internal Symmetry, Acta Phys. Austriaca 41 (1975) 409 [INSPIRE].
  58. [58]
    W. Siegel, Superfields in Higher Dimensional Space-time, Phys. Lett. 80B (1979) 220 [INSPIRE].
  59. [59]
    W. Siegel, Off-shell central charges, Nucl. Phys. B 173 (1980) 51 [INSPIRE].
  60. [60]
    M.F. Sohnius, K.S. Stelle and P.C. West, Representations of extended supersymmetry, in Superspace and Supergravity, S.W. Hawking and M. Roček eds., Cambridge Unieversity Press, (1981), p. 283.Google Scholar
  61. [61]
    M. Müller, Chiral Actions for Minimal N = 2 Supergravity, Nucl. Phys. B 289 (1987) 557 [INSPIRE].
  62. [62]
    B. de Wit, R. Philippe and A. Van Proeyen, The Improved Tensor Multiplet in N = 2 Supergravity, Nucl. Phys. B 219 (1983) 143 [INSPIRE].
  63. [63]
    U. Lindström and M. Roček, Scalar Tensor Duality and N = 1, 2 Nonlinear σ-models, Nucl. Phys. B 222 (1983) 285 [INSPIRE].
  64. [64]
    W. Siegel, Chiral Actions for N = 2 Supersymmetric Tensor Multiplets, Phys. Lett. 153B (1985) 51 [INSPIRE].
  65. [65]
    J.A. Bagger, A.S. Galperin, E.A. Ivanov and V.I. Ogievetsky, Gauging N = 2 σ Models in Harmonic Superspace, Nucl. Phys. B 303 (1988) 522 [INSPIRE].
  66. [66]
    M. Müller, Consistent Classical Supergravity Theories, Lect. Notes Phys. 336 (1989).Google Scholar
  67. [67]
    S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Different representations for the action principle in 4D N = 2 supergravity, JHEP 04 (2009) 007 [arXiv:0812.3464] [INSPIRE].
  68. [68]
    D. Butter and S.M. Kuzenko, N = 2 AdS supergravity and supercurrents, JHEP 07 (2011) 081 [arXiv:1104.2153] [INSPIRE].
  69. [69]
    S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Field theory in 4D N = 2 conformally flat superspace, JHEP 10 (2008) 001 [arXiv:0807.3368] [INSPIRE].
  70. [70]
    S. Deser and B. Zumino, Broken Supersymmetry and Supergravity, Phys. Rev. Lett. 38 (1977) 1433 [INSPIRE].
  71. [71]
    U. Lindström and M. Roček, Constrained local superfields, Phys. Rev. D 19 (1979) 2300 [INSPIRE].
  72. [72]
    S.M. Kuzenko, Superconformal vector multiplet self-couplings and generalised Fayet-Iliopoulos terms, Phys. Lett. B 795 (2019) 37 [arXiv:1904.05201] [INSPIRE].
  73. [73]
    Y. Aldabergenov and S.V. Ketov, Removing instability of inflation in Polonyi-Starobinsky supergravity by adding FI term, Mod. Phys. Lett. A 91 (2018) 1850032 [arXiv:1711.06789] [INSPIRE].
  74. [74]
    F. Farakos, A. Kehagias and A. Riotto, Liberated \( \mathcal{N}=1 \) supergravity, JHEP 06 (2018) 011 [arXiv:1805.01877] [INSPIRE].
  75. [75]
    R. Ishikawa and S.V. Ketov, Gravitino condensate in N = 1 supergravity coupled to the N = 1 supersymmetric Born-Infeld theory, arXiv:1904.08586 [INSPIRE].
  76. [76]
    Y. Aldabergenov, S.V. Ketov and R. Knoops, General couplings of a vector multiplet in N = 1 supergravity with new FI terms, Phys. Lett. B 785 (2018) 284 [arXiv:1806.04290] [INSPIRE].
  77. [77]
    H. Abe, Y. Aldabergenov, S. Aoki and S.V. Ketov, Massive vector multiplet with Dirac-Born-Infeld and new Fayet-Iliopoulos terms in supergravity, JHEP 09 (2018) 094 [arXiv:1808.00669] [INSPIRE].
  78. [78]
    N. Cribiori, F. Farakos and M. Tournoy, Supersymmetric Born-Infeld actions and new Fayet-Iliopoulos terms, JHEP 03 (2019) 050 [arXiv:1811.08424] [INSPIRE].
  79. [79]
    Y. Aldabergenov, No-scale supergravity with new Fayet-Iliopoulos term, Phys. Lett. B 795 (2019) 366 [arXiv:1903.11829] [INSPIRE].
  80. [80]
    A. Ceresole, G. Dall’Agata, S. Ferrara, M. Trigiante and A. Van Proeyen, A search for an \( \mathcal{N}=2 \) inflaton potential, Fortsch. Phys. 62 (2014) 584 [arXiv:1404.1745] [INSPIRE].
  81. [81]
    S.J. Gates Jr., 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].
  82. [82]
    A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace, Class. Quant. Grav. 1 (1984) 469 [Erratum ibid. 2 (1985) 127] [INSPIRE].
  83. [83]
    A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic Superspace, Cambridge University Press, (2001).Google Scholar
  84. [84]
    A.S. Galperin, N.A. Ky and E. Sokatchev, N = 2 Supergravity in Superspace: Solution to the Constraints, Class. Quant. Grav. 4 (1987) 1235 [INSPIRE].
  85. [85]
    A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E. Sokatchev, N = 2 Supergravity in Superspace: Different Versions and Matter Couplings, Class. Quant. Grav. 4 (1987) 1255 [INSPIRE].
  86. [86]
    S.M. Kuzenko, U. Lindström, M. Roček and G. Tartaglino-Mazzucchelli, 4D N = 2 Supergravity and Projective Superspace, JHEP 09 (2008) 051 [arXiv:0805.4683] [INSPIRE].
  87. [87]
    S.M. Kuzenko, U. Lindström, M. Roček and G. Tartaglino-Mazzucchelli, On conformal supergravity and projective superspace, JHEP 08 (2009) 023 [arXiv:0905.0063] [INSPIRE].
  88. [88]
    D. Butter, New approach to curved projective superspace, Phys. Rev. D 92 (2015) 085004 [arXiv:1406.6235] [INSPIRE].
  89. [89]
    D. Butter, Projective multiplets and hyperkähler cones in conformal supergravity, JHEP 06 (2015) 161 [arXiv:1410.3604] [INSPIRE].
  90. [90]
    S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Five-dimensional Superfield Supergravity, Phys. Lett. B 661 (2008) 42 [arXiv:0710.3440] [INSPIRE].
  91. [91]
    S.M. Kuzenko and G. Tartaglino-Mazzucchelli, 5D Supergravity and Projective Superspace, JHEP 02 (2008) 004 [arXiv:0712.3102] [INSPIRE].
  92. [92]
    S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Super-Weyl invariance in 5D supergravity, JHEP 04 (2008) 032 [arXiv:0802.3953] [INSPIRE].
  93. [93]
    G. Tartaglino-Mazzucchelli, 2D N = (4,4) superspace supergravity and bi-projective superfields, JHEP 04 (2010) 034 [arXiv:0911.2546] [INSPIRE].
  94. [94]
    G. Tartaglino-Mazzucchelli, On 2D N=(4,4) superspace supergravity, Phys. Part. Nucl. Lett. 8 (2011) 251 [arXiv:0912.5300] [INSPIRE].
  95. [95]
    S.M. Kuzenko, U. Lindström and G. Tartaglino-Mazzucchelli, Off-shell supergravity-matter couplings in three dimensions, JHEP 03 (2011) 120 [arXiv:1101.4013] [INSPIRE].
  96. [96]
    W.D. Linch, III and G. Tartaglino-Mazzucchelli, Six-dimensional Supergravity and Projective Superfields, JHEP 08 (2012) 075 [arXiv:1204.4195] [INSPIRE].
  97. [97]
    E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
  98. [98]
    S. Ferrara, L. Girardello and M. Porrati, Spontaneous breaking of N = 2 to N = 1 in rigid and local supersymmetric theories, Phys. Lett. B 376 (1996) 275 [hep-th/9512180] [INSPIRE].
  99. [99]
    I. Antoniadis, J.-P. Derendinger, P.M. Petropoulos and K. Siampos, All partial breakings in \( \mathcal{N}=2 \) supergravity with a single hypermultiplet, JHEP 08 (2018) 045 [arXiv:1806.09639] [INSPIRE].
  100. [100]
    I. Antoniadis, J.-P. Derendinger and J.-C. Jacot, N = 2 supersymmetry breaking at two different scales, Nucl. Phys. B 863 (2012) 471 [arXiv:1204.2141] [INSPIRE].
  101. [101]
    D. Butter, N = 1 Conformal Superspace in Four Dimensions, Annals Phys. 325 (2010) 1026 [arXiv:0906.4399] [INSPIRE].
  102. [102]
    T. Kugo and S. Uehara, N = 1 Superconformal Tensor Calculus: Multiplets With External Lorentz Indices and Spinor Derivative Operators, Prog. Theor. Phys. 73 (1985) 235 [INSPIRE].
  103. [103]
    T. Kugo, R. Yokokura and K. Yoshioka, Component versus superspace approaches to D = 4, N = 1 conformal supergravity, PTEP 2016 (2016) 073B07 [arXiv:1602.04441] [INSPIRE].
  104. [104]
    D. Butter, S.M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, Conformal supergravity in three dimensions: New off-shell formulation, JHEP 09 (2013) 072 [arXiv:1305.3132] [INSPIRE].
  105. [105]
    D. Butter, S.M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, Conformal supergravity in five dimensions: New approach and applications, JHEP 02 (2015) 111 [arXiv:1410.8682] [INSPIRE].
  106. [106]
    D. Butter, S.M. Kuzenko, J. Novak and S. Theisen, Invariants for minimal conformal supergravity in six dimensions, JHEP 12 (2016) 072 [arXiv:1606.02921] [INSPIRE].
  107. [107]
    D. Butter, J. Novak and G. Tartaglino-Mazzucchelli, The component structure of conformal supergravity invariants in six dimensions, JHEP 05 (2017) 133 [arXiv:1701.08163] [INSPIRE].
  108. [108]
    P.S. Howe, A Superspace Approach To Extended Conformal Supergravity, Phys. Lett. 100B (1981) 389 [INSPIRE].

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Albert Einstein Center for Fundamental Physics, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland
  2. 2.Laboratoire de Physique Théorique et Hautes Énergies — LPTHESorbonne Université, CNRSParisFrance
  3. 3.KU Leuven, Institute for Theoretical PhysicsLeuvenBelgium

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