Abstract
We propose a nilpotent \( \mathcal{N}=1 \) tensor multiplet describing two fields, which are the Goldstino and the axion, the latter being realised in terms of the field strength of a gauge two-form. This supersymmetric multiplet is formulated in terms of a deformed real linear superfield, subject to a cubic nilpotency condition. Its couplings to a super Yang-Mills multiplet and supergravity are presented. To define a nilpotent tensor multiplet in the locally supersymmetric case, one has to make use of either real or complex three-form supergravity theories, which are variant realisations of the old minimal formulation for \( \mathcal{N}=1 \) supergravity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I. Antoniadis, E. Dudas, S. Ferrara and A. Sagnotti, The Volkov-Akulov-Starobinsky supergravity, Phys. Lett. B 733 (2014) 32 [arXiv:1403.3269] [INSPIRE].
S. Ferrara, R. Kallosh and A. Linde, Cosmology with nilpotent superfields, JHEP 10 (2014) 143 [arXiv:1408.4096] [INSPIRE].
G. Dall’Agata and F. Zwirner, On sgoldstino-less supergravity models of inflation, JHEP 12 (2014) 172 [arXiv:1411.2605] [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 [arXiv:1507.08264] [INSPIRE].
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].
S.M. Kuzenko, Complex linear Goldstino superfield and supergravity, JHEP 10 (2015) 006 [arXiv:1508.03190] [INSPIRE].
R. Kallosh and T. Wrase, de Sitter supergravity model building, Phys. Rev. D 92 (2015) 105010 [arXiv:1509.02137] [INSPIRE].
M. Schillo, E. van der Woerd and T. Wrase, The general de Sitter supergravity component action, Fortsch. Phys. 64 (2016) 292 [arXiv:1511.01542] [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].
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].
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].
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].
E.I. Buchbinder and S.M. Kuzenko, Three-form multiplet and supersymmetry breaking, JHEP 09 (2017) 089 [arXiv:1705.07700] [INSPIRE].
U. Lindström and M. Roček, Constrained local superfields, Phys. Rev. D 19 (1979) 2300 [INSPIRE].
M. Roček, Linearizing the Volkov-Akulov model, Phys. Rev. Lett. 41 (1978) 451 [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. Samuel and J. Wess, A superfield formulation of the nonlinear realization of supersymmetry and its coupling to supergravity, Nucl. Phys. B 221 (1983) 153 [INSPIRE].
S.M. Kuzenko and S.J. Tyler, Complex linear superfield as a model for Goldstino, JHEP 04 (2011) 057 [arXiv:1102.3042] [INSPIRE].
D.V. Volkov and V.P. Akulov, Possible universal neutrino interaction, JETP Lett. 16 (1972) 438 [INSPIRE].
D.V. Volkov and V.P. Akulov, Is the Neutrino a Goldstone Particle?, Phys. Lett. B 46 (1973) 109 [INSPIRE].
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].
P. Nath, Supersymmetry, supergravity, and unification, Cambridge University Press, (2017).
E.A. Ivanov and A.A. Kapustnikov, General relationship between linear and nonlinear realizations of supersymmetry, J. Phys. A 11 (1978) 2375 [INSPIRE].
S.M. Kuzenko and S.J. Tyler, On the Goldstino actions and their symmetries, JHEP 05 (2011) 055 and supplementary material [arXiv:1102.3043] [INSPIRE].
S.M. Kuzenko and S.J. Tyler, Comments on the complex linear Goldstino superfield, arXiv:1507.04593 [INSPIRE].
F. Farakos, O. Hulık, P. Kočí and R. von Unge, Non-minimal scalar multiplets, supersymmetry breaking and dualities, JHEP 09 (2015) 177 [arXiv:1507.01885] [INSPIRE].
S. Ferrara, J. Wess and B. Zumino, Supergauge multiplets and superfields, Phys. Lett. B 51 (1974) 239 [INSPIRE].
W. Siegel, Gauge spinor superfield as a scalar multiplet, Phys. Lett. B 85 (1979) 333 [INSPIRE].
Y. Kahn, D.A. Roberts and J. Thaler, The goldstone and goldstino of supersymmetric inflation, JHEP 10 (2015) 001 [arXiv:1504.05958] [INSPIRE].
S. Ferrara, R. Kallosh and J. Thaler, Cosmology with orthogonal nilpotent superfields, Phys. Rev. D 93 (2016) 043516 [arXiv:1512.00545] [INSPIRE].
J.J.M. Carrasco, R. Kallosh and A. Linde, Minimal supergravity inflation, Phys. Rev. D 93 (2016) 061301 [arXiv:1512.00546] [INSPIRE].
G. Dall’Agata and F. Farakos, Constrained superfields in supergravity, JHEP 02 (2016) 101 [arXiv:1512.02158] [INSPIRE].
E. Dudas, S. Ferrara and A. Sagnotti, A superfield constraint for \( \mathcal{N}=2\to \mathcal{N}=0 \) breaking, JHEP 08 (2017) 109 [arXiv:1707.03414] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, New nilpotent \( \mathcal{N}=2 \) superfields, Phys. Rev. D 97 (2018) 026003 [arXiv:1707.07390] [INSPIRE].
U. Lindström and M. Roček, Scalar tensor duality and N = 1, N = 2 nonlinear σ-models, Nucl. Phys. B 222 (1983) 285 [INSPIRE].
B. de Wit and M. Roček, Improved tensor multiplets, Phys. Lett. B 109 (1982) 439 [INSPIRE].
S.J. Gates Jr., Super p-form gauge superfields, Nucl. Phys. B 184 (1981) 381 [INSPIRE].
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].
P. Binetruy, G. Girardi and R. Grimm, Supergravity couplings: a geometric formulation, Phys. Rept. 343 (2001) 255 [hep-th/0005225] [INSPIRE].
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].
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)).
R. Grimm, J. Wess and B. Zumino, Consistency checks on the superspace formulation of supergravity, Phys. Lett. B 73 (1978) 415 [INSPIRE].
R. Grimm, J. Wess and B. Zumino, A complete solution of the Bianchi identities in superspace, Nucl. Phys. B 152 (1979) 255 [INSPIRE].
J. Wess and B. Zumino, Superfield Lagrangian for supergravity, Phys. Lett. B 74 (1978) 51 [INSPIRE].
B. Zumino, Supergravity and superspace, in Recent developments in gravitation — Cargèse 1978, M. Lévy and S. Deser eds., Plenum Press, N.Y., U.S.A., (1979), pp. 405-459.
K.S. Stelle and P.C. West, Minimal auxiliary fields for supergravity, Phys. Lett. B 74 (1978) 330 [INSPIRE].
S. Ferrara and P. van Nieuwenhuizen, The auxiliary fields of supergravity, Phys. Lett. B 74 (1978) 333 [INSPIRE].
P.S. Howe and R.W. Tucker, Scale invariance in superspace, Phys. Lett. B 80 (1978) 138 [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Complex three-form supergravity and membranes, JHEP 12 (2017) 005 [arXiv:1710.00535] [INSPIRE].
S.J. Gates Jr. and W. Siegel, Variant superfield representations, Nucl. Phys. B 187 (1981) 389 [INSPIRE].
B.A. Ovrut and D. Waldram, Membranes and three form supergravity, Nucl. Phys. B 506 (1997) 236 [hep-th/9704045] [INSPIRE].
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].
F. Farakos, S. Lanza, L. Martucci and D. Sorokin, Three-forms in supergravity and flux compactifications, Eur. Phys. J. C 77 (2017) 602 [arXiv:1706.09422] [INSPIRE].
B.B. Deo and S.J. Gates Jr., Comments on nonminimal N = 1 scalar multiplets, Nucl. Phys. B 254 (1985) 187 [INSPIRE].
D. Butter and S.M. Kuzenko, A dual formulation of supergravity-matter theories, Nucl. Phys. B 854 (2012) 1 [arXiv:1106.3038] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Three-dimensional N = 2 (AdS) supergravity and associated supercurrents, JHEP 12 (2011) 052 [arXiv:1109.0496] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1712.09258
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Kuzenko, S.M. Nilpotent \( \mathcal{N}=1 \) tensor multiplet. J. High Energ. Phys. 2018, 131 (2018). https://doi.org/10.1007/JHEP04(2018)131
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2018)131