Abstract
Recently, a nilpotent real scalar superfield V was introduced in [1] as a model for the Goldstino. It contains only two independent component fields, the Goldstino and the auxiliary D-field. Here we first show that V can equivalently be realised as a constrained three-form superfield. We demonstrate that every irreducible Goldstino superfield (of which the Goldstino is the only independent component field) can be realised as a descendant of V which is invariant under local rescalings V → eτ V, where τ is an arbitrary real scalar superfield. We next propose a new Goldstino supermultiplet which is described by a nilpotent three-form superfield \( \mathcal{Y} \) that is a variant formulation for the nilpotent chiral superfield, which is often used in off-shell models for spontaneously broken supergravity. It is shown that the action describing the dynamics of \( \mathcal{Y} \) may be obtained from a super-symmetric nonlinear σ-model in the infrared limit. Unlike V , the Goldstino superfield \( \mathcal{Y} \) contains two independent auxiliary fields, F = H + iG, of which H is a scalar and G is the field strength of a gauge three-form. When \( \mathcal{Y} \) is coupled to supergravity, both H and G produce positive contributions to the cosmological constant. While the contribution from H is uniquely determined by the parameter of the supersymmetry breaking in the action, the contribution from G is dynamical.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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].
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].
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, Complex linear superfield as a model for Goldstino, JHEP 04 (2011) 057 [arXiv:1102.3042] [INSPIRE].
P. Fayet and J. Iliopoulos, Spontaneously broken supergauge symmetries and Goldstone spinors, Phys. Lett. 51B (1974) 461 [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].
P.K. Townsend, Cosmological constant in supergravity, Phys. Rev. D 15 (1977) 2802 [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].
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 [INSPIRE].
S. Deser and B. Zumino, Broken supersymmetry and supergravity, Phys. Rev. Lett. 38 (1977) 1433 [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.J. Gates, Jr., Super p form gauge superfields, Nucl. Phys. B 184 (1981) 381 [INSPIRE].
S.J. Gates, Jr. and W. Siegel, Variant superfield representations, Nucl. Phys. B 187 (1981) 389 [INSPIRE].
S.J. Gates, 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.A. Batalin and G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators, Phys. Rev. D 28 (1983) 2567 [Erratum ibid. D 30 (1984) 508] [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].
I.L. Buchbinder and S.M. Kuzenko, Ideas and methods of supersymmetry and supergravity or a walk through superspace, IOP, Bristol, U.K. (1995), revised edition (1998).
D.V. Volkov and V.P. Akulov, Possible universal neutrino interaction, JETP Lett. 16 (1972) 438 [Pisma Zh. Eksp. Teor. Fiz. 16 (1972) 621] [INSPIRE].
D.V. Volkov and V.P. Akulov, Is the neutrino a Goldstone particle?, Phys. Lett. 46B (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].
S.M. Kuzenko and S.J. Tyler, On the Goldstino actions and their symmetries, JHEP 05 (2011) 055 [arXiv:1102.3043] [INSPIRE].
S.M. Kuzenko and I.N. McArthur, Goldstino superfields for spontaneously broken N = 2 supersymmetry, JHEP 06 (2011) 133 [arXiv:1105.3001] [INSPIRE].
M.J. Duncan and L.G. Jensen, Four forms and the vanishing of the cosmological constant, Nucl. Phys. B 336 (1990) 100 [INSPIRE].
K. Groh, J. Louis and J. Sommerfeld, Duality and couplings of 3-form-multiplets in N = 1 supersymmetry, JHEP 05 (2013) 001 [arXiv:1212.4639] [INSPIRE].
W. Siegel, A polynomial action for a massive, self-interacting chiral superfield coupled to supergravity, HUTP-77/A077 (1977).
M. Kaku and P.K. Townsend, Poincaré supergravity as broken superconformal gravity, Phys. Lett. 76B (1978) 54 [INSPIRE].
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].
R. Grimm, J. Wess and B. Zumino, Consistency checks on the superspace formulation of supergravity, Phys. Lett. 73B (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. 74B (1978) 51 [INSPIRE].
K.S. Stelle and P.C. West, Minimal auxiliary fields for supergravity, Phys. Lett. 74B (1978) 330 [INSPIRE].
S. Ferrara and P. van Nieuwenhuizen, The auxiliary fields of supergravity, Phys. Lett. 74B (1978) 333 [INSPIRE].
P.S. Howe and R.W. Tucker, Scale invariance in superspace, Phys. Lett. 80B (1978) 138 [INSPIRE].
T. Kugo and S. Uehara, Improved superconformal gauge conditions in the N = 1 supergravity Yang-Mills matter system, Nucl. Phys. B 222 (1983) 125 [INSPIRE].
S. Ferrara and P. van Nieuwenhuizen, Tensor calculus for supergravity, Phys. Lett. B 76 (1978) 404.
W. Siegel, Solution to constraints in Wess-Zumino supergravity formalism, Nucl. Phys. B 142 (1978) 301 [INSPIRE].
D. Butter and S.M. Kuzenko, A dual formulation of supergravity-matter theories, Nucl. Phys. B 854 (2012) 1 [arXiv:1106.3038] [INSPIRE].
M.F. Sohnius and P.C. West, An alternative minimal off-shell version of N = 1 supergravity, Phys. Lett. 105B (1981) 353 [INSPIRE].
M.F. Sohnius and P.C. West, The new minimal formulation of N = 1 supergravity and its tensor calculus, in Quantum structure of space and Time, M.J. Duff and C.J. Isham eds., Cambridge University Press, Cambridge U.K. (1982).
M. Sohnius and P.C. West, The tensor calculus and matter coupling of the alternative minimal auxiliary field formulation of N = 1 supergravity, Nucl. Phys. B 198 (1982) 493 [INSPIRE].
W. Siegel and S.J. Gates Jr., Superfield supergravity, Nucl. Phys. B 147 (1979) 77 [INSPIRE].
P. Binetruy, F. Pillon, G. Girardi and R. Grimm, The three form multiplet in supergravity, Nucl. Phys. B 477 (1996) 175 [hep-th/9603181] [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].
I.A. Bandos and C. Meliveo, Supermembrane interaction with dynamical D = 4 N = 1 supergravity. Superfield Lagrangian description and spacetime equations of motion, JHEP 08 (2012) 140 [arXiv:1205.5885] [INSPIRE].
V. Ogievetsky and E. Sokatchev, Equation of motion for the axial gravitational superfield, Sov. J. Nucl. Phys. 32 (1980) 589 [Yad. Fiz. 32 (1980) 1142] [INSPIRE].
M.J. Duff and P. van Nieuwenhuizen, Quantum inequivalence of different field representations, Phys. Lett. B 94 (1980) 179.
A. Aurilia, H. Nicolai and P.K. Townsend, Hidden constants: the theta parameter of QCD and the cosmological constant of N = 8 supergravity, Nucl. Phys. B 176 (1980) 509 [INSPIRE].
S.W. Hawking, The cosmological constant is probably zero, Phys. Lett. B 134 (1984) 403.
M.J. Duff, The cosmological constant is possibly zero, but the proof is probably wrong, Phys. Lett. B 226 (1989) 36 [INSPIRE].
R. Bousso and J. Polchinski, Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [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].
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: 1705.07700
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Buchbinder, E.I., Kuzenko, S.M. Three-form multiplet and supersymmetry breaking. J. High Energ. Phys. 2017, 89 (2017). https://doi.org/10.1007/JHEP09(2017)089
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2017)089