Abstract
Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-Stückelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Nagy, A. Padilla and I. Zavala, The super-Stückelberg procedure and dS in pure supergravity, Proc. Roy. Soc. Lond. A 476 (2020) 20200035 [arXiv:1910.14349] [INSPIRE].
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].
E. Dudas, S. Ferrara, A. Kehagias and A. Sagnotti, Properties of nilpotent supergravity, JHEP 09 (2015) 217 [arXiv:1507.07842] [INSPIRE].
E.A. Bergshoeff, D.Z. Freedman, R. Kallosh and A. Van Proeyen, Pure de Sitter supergravity, Phys. Rev. D 92 (2015) 085040 [Erratum ibid. 93 (2016) 069901] [arXiv:1507.08264] [INSPIRE].
F. Hasegawa and Y. Yamada, Component action of nilpotent multiplet coupled to matter in 4 dimensional N = 1 supergravity, JHEP 10 (2015) 106 [arXiv:1507.08619] [INSPIRE].
S. Ferrara, M. Porrati and A. Sagnotti, Scale invariant Volkov-Akulov supergravity, Phys. Lett. B 749 (2015) 589 [arXiv:1508.02939] [INSPIRE].
S.M. Kuzenko, Complex linear Goldstino superfield and supergravity, JHEP 10 (2015) 006 [arXiv:1508.03190] [INSPIRE].
I. Antoniadis and C. Markou, The coupling of non-linear supersymmetry to supergravity, Eur. Phys. J. C 75 (2015) 582 [arXiv:1508.06767] [INSPIRE].
M. Roček, Linearizing the Volkov-Akulov model, Phys. Rev. Lett. 41 (1978) 451 [INSPIRE].
U. Lindström and M. Roček, Constrained local superfields, Phys. Rev. D 19 (1979) 2300 [INSPIRE].
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].
Z. Komargodski and N. Seiberg, From linear SUSY to constrained superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].
S.M. Kuzenko and S.J. Tyler, On the Goldstino actions and their symmetries, JHEP 05 (2011) 055 [arXiv:1102.3043] [INSPIRE].
H. Nishino and S. Rajpoot, Unimodular supergravity, Phys. Lett. B 528 (2002) 259 [hep-th/0107202] [INSPIRE].
L. Baulieu, Unimodular gauge in perturbative gravity and supergravity, Phys. Lett. B 808 (2020) 135591 [arXiv:2004.05950] [INSPIRE].
J. Anero, C.P. Martin and R. Santos-Garcia, Off-shell unimodular N = 1, d = 4 supergravity, JHEP 01 (2020) 145 [arXiv:1911.04160] [INSPIRE].
J. Anero, C.P. Martin and R. Santos-Garcia, A note on unimodular N = 1, d = 4 AdS supergravity, JCAP 03 (2020) 006 [arXiv:2001.05365] [INSPIRE].
J. Wess and B. Zumino, Superfield Lagrangian for supergravity, Phys. Lett. B 74 (1978) 51 [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton, NJ, U.S.A. (1992).
I.L. Buchbinder and S.M. Kuzenko, Ideas and methods of supersymmetry and supergravity: or a walk through superspace, IOP, Bristol, U.K. (1998).
I. Bandos, M. Heller, S.M. Kuzenko, L. Martucci and D. Sorokin, The goldstino brane, the constrained superfields and matter in N = 1 supergravity, JHEP 11 (2016) 109 [arXiv:1608.05908] [INSPIRE].
E.C.G. Stueckelberg, Interaction energy in electrodynamics and in the field theory of nuclear forces, Helv. Phys. Acta 11 (1938) 225 [INSPIRE].
J.J. van der Bij, H. van Dam and Y.J. Ng, The exchange of massless spin two particles, Physica A 116 (1982) 307 [INSPIRE].
W. Buchmüller and N. Dragon, Einstein gravity from restricted coordinate invariance, Phys. Lett. B 207 (1988) 292 [INSPIRE].
W. Buchmüller and N. Dragon, Gauge fixing and the cosmological constant, Phys. Lett. B 223 (1989) 313 [INSPIRE].
M. Henneaux and C. Teitelboim, The cosmological constant and general covariance, Phys. Lett. B 222 (1989) 195 [INSPIRE].
K.V. Kuchar, Does an unspecified cosmological constant solve the problem of time in quantum gravity?, Phys. Rev. D 43 (1991) 3332 [INSPIRE].
G.F.R. Ellis, H. van Elst, J. Murugan and J.-P. Uzan, On the trace-free Einstein equations as a viable alternative to general relativity, Class. Quant. Grav. 28 (2011) 225007 [arXiv:1008.1196] [INSPIRE].
B. Fiol and J. Garriga, Semiclassical unimodular gravity, JCAP 08 (2010) 015 [arXiv:0809.1371] [INSPIRE].
A. Padilla and I.D. Saltas, A note on classical and quantum unimodular gravity, Eur. Phys. J. C 75 (2015) 561 [arXiv:1409.3573] [INSPIRE].
G. Dall’Agata, S. Ferrara and F. Zwirner, Minimal scalar-less matter-coupled supergravity, Phys. Lett. B 752 (2016) 263 [arXiv:1509.06345] [INSPIRE].
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].
N. Cribiori, G. Dall’Agata, F. Farakos and M. Porrati, Minimal constrained supergravity, Phys. Lett. B 764 (2017) 228 [arXiv:1611.01490] [INSPIRE].
S. Melville, D. Roest and D. Stefanyszyn, UV constraints on massive spinning particles: lessons from the gravitino, JHEP 02 (2020) 185 [arXiv:1911.03126] [INSPIRE].
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].
D.V. Volkov and V.A. Soroka, Gauge fields for symmetry group with spinor parameters, Theor. Math. Phys. 20 (1974) 829 [Teor. Mat. Fiz. 20 (1974) 291] [INSPIRE].
D.V. Volkov, Supergravity before 1976, in International conference on history of original ideas and basic discoveries in particle physics, (1994) [hep-th/9410024] [INSPIRE].
P. Van Nieuwenhuizen, Supergravity, Phys. Rept. 68 (1981) 189 [INSPIRE].
S.Y. Li, Y.-C. Qiu and S.-H. Henry Tye, Standard Model from a supergravity model with a naturally small cosmological constant, arXiv:2010.10089 [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge Univ. Press, Cambridge, U.K. (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2010.13758
Rights and permissions
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.
About this article
Cite this article
Bansal, S., Nagy, S., Padilla, A. et al. Unimodular vs nilpotent superfield approach to pure dS supergravity. J. High Energ. Phys. 2021, 146 (2021). https://doi.org/10.1007/JHEP01(2021)146
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2021)146