Abstract
We give a new expression for the supercurrent and its conservation in curved \( \mathcal{N} \) =1, D = 4 superspace using the superconformal approach. The first component of the superfield, whose lowest component is the vector auxiliary field gives the (super)Einstein equations. Its trace and couplings to conformal and non-conformal matter are presented. In a suitable dilatational gauge, the conformal gauge, we obtain an update of the Callan-Coleman-Jackiw improved currents for conformal matter, containing R-symmetry corrections for a new traceless covariantly conserved energy-momentum tensor. We observe that in the Poincaré gauge, where standard Poincaré supergravity is usually formulated, the currents are not improved and then the higher conformal symmetry of the matter sector is obscured. The curvature multiplets are used to find supersymmetric curved backgrounds and some examples are exhibited in agreement with existing results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C.G. Callan Jr., S.R. Coleman and R. Jackiw, A new improved energy-momentum tensor, Annals Phys. 59 (1970) 42 [INSPIRE].
S. Ferrara and B. Zumino, Transformation Properties of the Supercurrent, Nucl. Phys. B 87 (1975) 207 [INSPIRE].
S. Ferrara and B. Zumino, Structure of Conformal Supergravity, Nucl. Phys. B 134 (1978) 301 [INSPIRE].
M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Gauge Theory of the Conformal and Superconformal Group, Phys. Lett. B 69 (1977) 304 [INSPIRE].
S. Ferrara, M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Gauging the Graded Conformal Group with Unitary Internal Symmetries, Nucl. Phys. B 129 (1977) 125 [INSPIRE].
M. Kaku and P.K. Townsend, Poincaré supergravity as broken superconformal gravity, Phys. Lett. B 76 (1978) 54 [INSPIRE].
M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Properties of Conformal Supergravity, Phys. Rev. D 17 (1978) 3179 [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, (2012).
J. Wess and B. Zumino, Superspace Formulation of Supergravity, Phys. Lett. B 66 (1977) 361 [INSPIRE].
J. Wess and B. Zumino, Superfield Lagrangian for Supergravity, Phys. Lett. B 74 (1978) 51 [INSPIRE].
J. Wess and B. Zumino, The Component Formalism Follows From the Superspace Formulation of Supergravity, Phys. Lett. B 79 (1978) 394 [INSPIRE].
R. Grimm, J. Wess and B. Zumino, A Complete Solution of the Bianchi Identities in Superspace, Nucl. Phys. B 152 (1979) 255 [INSPIRE].
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].
S. Ferrara and P. van Nieuwenhuizen, The Auxiliary Fields of Supergravity, Phys. Lett. B 74 (1978) 333 [INSPIRE].
K.S. Stelle and P.C. West, Minimal Auxiliary Fields for Supergravity, Phys. Lett. B 74 (1978) 330 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, S Matrix for Theories That Admit Closure of the Algebra With the Aid of Auxiliary Fields: The Auxiliary Fields in Supergravity, Lett. Nuovo Cim. 22 (1978) 651 [INSPIRE].
G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
T.T. Dumitrescu, G. Festuccia and N. Seiberg, Exploring Curved Superspace, JHEP 08 (2012) 141 [arXiv:1205.1115] [INSPIRE].
T.E. Clark and S.T. Love, The supercurrent in supersymmetric field theories, Int. J. Mod. Phys. A 11 (1996) 2807 [hep-th/9506145] [INSPIRE].
Z. Komargodski and N. Seiberg, From Linear SUSY to Constrained Superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].
Z. Komargodski and N. Seiberg, Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [INSPIRE].
S.M. Kuzenko, Variant supercurrent multiplets, JHEP 04 (2010) 022 [arXiv:1002.4932] [INSPIRE].
S.M. Kuzenko, Variant supercurrents and Noether procedure, Eur. Phys. J. C 71 (2011) 1513 [arXiv:1008.1877] [INSPIRE].
Y. Korovin, S.M. Kuzenko and S. Theisen, The conformal supercurrents in diverse dimensions and conserved superconformal currents, JHEP 05 (2016) 134 [arXiv:1604.00488] [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].
S. Ferrara, R. Kallosh, A. Van Proeyen and T. Wrase, Linear Versus Non-linear Supersymmetry, in General, JHEP 04 (2016) 065 [arXiv:1603.02653] [INSPIRE].
P.K. Townsend and P. van Nieuwenhuizen, Anomalies, Topological Invariants and the Gauss-Bonnet Theorem in Supergravity, Phys. Rev. D 19 (1979) 3592 [INSPIRE].
S. Ferrara and M. Villasante, Curvatures, Gauss-Bonnet and Chern-Simons Multiplets in Old Minimal N = 1 Supergravity, J. Math. Phys. 30 (1989) 104 [INSPIRE].
S. Ferrara and S. Sabharwal, Structure of New Minimal Supergravity, Annals Phys. 189 (1989) 318 [INSPIRE].
S. Ferrara, S. Sabharwal and M. Villasante, Curvatures and Gauss-Bonnet Theorem in New Minimal Supergravity, Phys. Lett. B 205 (1988) 302 [INSPIRE].
B. Vanhecke and A. Van Proeyen, Covariant field equations in supergravity, arXiv:1705.06675 [INSPIRE].
S. Ferrara and P. van Nieuwenhuizen, Tensor Calculus for Supergravity, Phys. Lett. B 76 (1978) 404 [INSPIRE].
T. Kugo and S. Uehara, Conformal and Poincaré Tensor Calculi in N = 1 Supergravity, Nucl. Phys. B 226 (1983) 49 [INSPIRE].
P.K. Townsend, Cosmological Constant in Supergravity, Phys. Rev. D 15 (1977) 2802 [INSPIRE].
S. Ferrara, M.T. Grisaru and P. van Nieuwenhuizen, Poincaré and Conformal Supergravity Models With Closed Algebras, Nucl. Phys. B 138 (1978) 430 [INSPIRE].
I. Antoniadis, E. Dudas, S. Ferrara and A. Sagnotti, The Volkov-Akulov-Starobinsky supergravity, Phys. Lett. B 733 (2014) 32 [arXiv:1403.3269] [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. D 93 (2016) 069901] [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].
E. Cremmer, S. Ferrara, C. Kounnas and D.V. Nanopoulos, Naturally Vanishing Cosmological Constant in N = 1 Supergravity, Phys. Lett. B 133 (1983) 61 [INSPIRE].
E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen, Yang-Mills Theories with Local Supersymmetry: Lagrangian, Transformation Laws and SuperHiggs Effect, Nucl. Phys. B 212 (1983) 413 [INSPIRE].
K.S. Stelle, Ultraviolet infinities and counterterms in supersymmetric theories, Int. J. Geom. Meth. Mod. Phys. 09 (2012) 1261013 [INSPIRE].
Z. Bern, Perturbative gravity from gauge theory, Mod. Phys. Lett. A 29 (2014) 1430036 [INSPIRE].
S. Ferrara, R. Kallosh and A. Linde, Cosmology with Nilpotent Superfields, JHEP 10 (2014) 143 [arXiv:1408.4096] [INSPIRE].
A. Sagnotti and S. Ferrara, Supersymmetry and Inflation, PoS(PLANCK 2015)113 [arXiv:1509.01500] [INSPIRE].
E. Bergshoeff, D. Freedman, R. Kallosh and A. Van Proeyen, Construction of the de Sitter supergravity, arXiv:1602.01678 [INSPIRE].
S. Ferrara, A. Kehagias and A. Sagnotti, Cosmology and Supergravity, Int. J. Mod. Phys. A 31 (2016) 1630044 [arXiv:1605.04791] [INSPIRE].
V. Pestun et al., Localization techniques in quantum field theories, arXiv:1608.02952 [INSPIRE].
S.S. Pufu, The F-Theorem and F-Maximization, arXiv:1608.02960 [INSPIRE].
E. Sezgin and Y. Tanii, Superconformal σ-models in higher than two-dimensions, Nucl. Phys. B 443 (1995) 70 [hep-th/9412163] [INSPIRE].
J. Wess and B. Zumino, A Lagrangian Model Invariant Under Supergauge Transformations, Phys. Lett. B 49 (1974) 52 [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: 1705.02272
Dedicated to the memory of Aurelio Grillo
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
Ferrara, S., Samsonyan, M., Tournoy, M. et al. The supercurrent and Einstein equations in the superconformal formulation. J. High Energ. Phys. 2017, 119 (2017). https://doi.org/10.1007/JHEP08(2017)119
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2017)119