Abstract
We review two off-shell models for spontaneously broken \(\mathcal{N} = 1\) and \(\mathcal{N} = 2\) supergravity proposed in arXiv:1702.02423 and arXiv:1707.07390. New results on nilpotent \(\mathcal{N} = 1\) supergravity are also included.
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Notes
Since Deser and Zumino [13] made use of on-shell supergravity, it was next to impossible to construct a complete supergravity-Goldstino action in their setting.
In curved superspace, the covariant derivatives \({{\mathcal{D}}_{A}} = ({{\mathcal{D}}_{a}},{{\mathcal{D}}_{\alpha }},{{\bar {\mathcal{D}}}^{{\dot {\alpha }}}})\) have the form \({{\mathcal{D}}_{A}} = E_{A}^{M}{{\partial }_{M}} + \tfrac{1}{2}\Omega _{A}^{{bc}}{{M}_{{bc}}},\) where \({{M}_{{bc}}}\) is the Lorentz generator. Our description of the old minimal formulation for \(\mathcal{N} = 1\) supergravity follows [19], where the graded commutation relations for the covariant derivatives are given.
These backgrounds are maximally supersymmetric solutions of pure \({{R}^{2}}\) supergravity [35].
REFERENCES
E. Ivanov and A. Kapustnikov, “General relationship between linear and nonlinear realisations of supersymmetry,” J. Phys. A 11, 2375 (1978); E. Ivanov and A. Kapustnikov, “The nonlinear realisation structure of models with spontaneously broken supersymmetry,” J. Phys. G 8, 167 (1982).
D. V. Volkov and V. P. Akulov, “Possible universal neutrino interaction,” JETP Lett. 16, 438 (1972);
D. V. Volkov and V. P. Akulov, “Is the neutrino a Goldstone particle?,” Phys. Lett. B 46, 109 (1973).
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,” J. High Energy Phys. 1611, 109 (2016).
M. Roček, “Linearizing the Volkov–Akulov model,” Phys. Rev. Lett. 41, 451 (1978).
R. Casalbuoni, S. De Curtis, D. Dominici, F. Feruglio, and R. Gatto, “Non-linear realization of supersymmetry algebra from supersymmetric constraint,” Phys. Lett. B 220, 569 (1989).
Z. Komargodski and N. Seiberg, “From linear SUSY to constrained superfields,” J. High Energy Phys. 0909, 066 (2009).
S. M. Kuzenko and S. J. Tyler, “Complex linear superfield as a model for Goldstino,” J. High Energy Phys. 1104, 057 (2011).
S. M. Kuzenko and S. J. Tyler, “Relating the Komargodski-Seiberg and Akulov–Volkov actions: Exact nonlinear field redefinition,” Phys. Lett. B 698, 319 (2011); S. M. Kuzenko and S. J. Tyler, “On the Goldstino actions and their symmetries,” J. High Energy Phys. 1105, 055 (2011).
S. Samuel and J. Wess, “A superfield formulation of the non-linear realization of supersymmetry and its coupling to supergravity,” Nucl. Phys. B 221, 153 (1983).
N. Cribiori, G. Dall’Agata, and F. Farakos, “Interactions of N Goldstini in superspace,” Phys. Rev. D 94, 065019 (2016).
E. I. Buchbinder and S. M. Kuzenko, “Three-form multiplet and supersymmetry breaking,” J. High Energy Phys. 1709, 089 (2017).
D. V. Volkov and V. A. Soroka, “Higgs effect for Goldstone particles with spin 1/2,” JETP Lett. 18, 312 (1973).
S. Deser and B. Zumino, “Broken supersymmetry and supergravity,” Phys. Rev. Lett. 38, 1433 (1977).
U. Lindström and M. Roček, “Constrained local superfields,” Phys. Rev. D 19, 2300 (1979).
E. A. Bergshoeff, D. Z. Freedman, R. Kallosh, and A. van Proeyen, “Pure de Sitter supergravity,” Phys. Rev. D 92, 085040 (2015).
F. Hasegawa and Y. Yamada, “Component action of nilpotent multiplet coupled to matter in 4 dimensional \(\mathcal{N} = 1\) supergravity,” J. High Energy Phys. 1510, 106 (2015).
S. M. Kuzenko, I. N. McArthur, G. Tartaglino-Mazzucchelli, “Goldstino superfields in N = 2 supergravity,” J. High Energy Phys. 1705, 061 (2017).
S. M. Kuzenko and G. Tartaglino-Mazzucchelli, “New nilpotent \(\mathcal{N} = 2\) superfields,” Phys. Rev. D 97, 026003 (2018); arXiv:1707.07390 [hep-th].
I. L. Buchbinder and S. M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity, or a Walk through Superspace (IOP, Bristol, 1995), Revised Edition 1998.
S. M. Kuzenko, “Complex linear Goldstino superfield and supergravity,” J. High Energy Phys. 1510, 006 (2015).
I. Bandos, L. Martucci, D. Sorokin, and M. Tonin, “Brane induced supersymmetry breaking and de Sitter supergravity,” J. High Energy Phys. 1602, 080 (2016).
E. Dudas, S. Ferrara, A. Kehagias, and A. Sagnotti, “Properties of nilpotent supergravity,” J. High Energy Phys. 1509, 217 (2015).
S. Cecotti, S. Ferrara, M. Porrati, and S. Sabharwal, “New minimal higher derivative supergravity coupled to matter,” Nucl. Phys. B 306, 160 (1988).
S. Ferrara, A. Kehagias, and M. Porrati, “\({{\mathcal{R}}^{2}}\) supergravity,” J. High Energy Phys. 1508, 001 (2015).
R. Grimm, M. Sohnius, and J. Wess, “Extended supersymmetry and gauge theories,” Nucl. Phys. B 133, 275 (1978).
P. S. Howe, “Supergravity in superspace,” Nucl. Phys. B 199, 309 (1982).
S. M. Kuzenko, U. Lindström, M. Roček, and G. Tartaglino-Mazzucchelli, “On conformal supergravity and projective superspace,” J. High Energy Phys. 0908, 023 (2009).
D. Butter and S. M. Kuzenko, “New higher-derivative couplings in 4D N = 2 supergravity,” J. High Energy Phys. 1103, 047 (2011).
S. M. Kuzenko, “Super-Weyl anomalies in N = 2 supergravity and (non)local effective actions,” J. High Energy Phys. 1310, 151 (2013).
S. M. Kuzenko and G. Tartaglino-Mazzucchelli, “Nilpotent chiral superfield in N = 2 supergravity and partial rigid supersymmetry breaking,” J. High Energy Phys. 1603, 092 (2016).
B. de Wit, R. Philippe, and A. van Proeyen, “The improved tensor multiplet in N = 2 supergravity,” Nucl. Phys. B 219, 143 (1983).
I. Antoniadis, H. Partouche, and T. R. Taylor, “Spontaneous breaking of N = 2 global supersymmetry,” Phys. Lett. B 372, 83 (1996).
E. A. Ivanov and B. M. Zupnik, “Modified N = 2 supersymmetry and Fayet-Iliopoulos terms,” Phys. At. Nucl. 62, 1043 (1999).
D. Butter, G. Inverso, and I. Lodato, “Rigid 4D \(\mathcal{N} = 2\) supersymmetric backgrounds and actions,” J. High Energy Phys. 1509, 088 (2015).
S. M. Kuzenko, “Maximally supersymmetric solutions of \({{R}^{2}}\) supergravity,” Phys. Rev. D 94, 065014 (2016).
C. R. Nappi and E. Witten, “A WZW model based on a non-semisimple group,” Phys. Rev. Lett. 71, 3751 (1993).
J. Bagger and A. Galperin, “A new Goldstone multiplet for partially broken supersymmetry,” Phys. Rev. D 55, 1091 (1997).
M. Roček and A. A. Tseytlin, “Partial breaking of global D = 4 supersymmetry, constrained superfields, and 3-brane actions,” Phys. Rev. D 59, 106001 (1999).
E. Dudas, S. Ferrara, and A. Sagnotti, “A superfield constraint for \(\mathcal{N} = 2 \to \mathcal{N}\) = 0 breaking,” J. High Energy Phys. 1708, 109 (2017).
ACKNOWLEDGMENTS
I am grateful to Ian McArthur and Gabriele Tartaglino-Mazzucchelli for collaboration on [17, 18] and comments on the manuscript. I thanks the organisers of the Workshop SQS’2017 for their warm hospitality in Dubna. The research presented in this work is supported in part by the Australian Research Council, project no. DP160103633.
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Kuzenko, S.M. Goldstino Superfields in Supergravity. Phys. Part. Nuclei 49, 841–846 (2018). https://doi.org/10.1134/S106377961805026X
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DOI: https://doi.org/10.1134/S106377961805026X