Abstract
We describe the linearized supergeometry of eleven dimensional supergravity with four off-shell local supersymmetries. We start with a background Minkowski 11D, N=1 superspace, and an additional ingredient of a global, constant, G2-structure which facilitates the definition of a 4|4 + 7 background superspace. A bottom-up construction of linear fluctuations of the geometric constituents (such as supervielbein, spin connection, and the super 3-form of 11D supergravity) is given in terms of 4D, N=1 prepotential superfields. This is complemented by a top-down description of the linearized supergeometry of the 4|4 + 7 superspace dealing directly with torsion, curvature, and Bianchi identities. Torsion constraints that (combined with the Bianchi identities) lead to the preceding prepotential expressions of the gauge fields are identified. All irreducible consequences of the torsion and 4-form Bianchi identities are systematically derived except for dimension 2 Bianchi identities of the 4-form, and dimension \( \frac{5}{2} \) Bianchi identities of torsion, which set bosonic curls of components of one lower dimension to zero.
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References
N. Berkovits, Super Poincaré covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035] [INSPIRE].
M. Cederwall, D = 11 supergravity with manifest supersymmetry, Mod. Phys. Lett. A 25 (2010) 3201 [arXiv:1001.0112] [INSPIRE].
N. Berkovits and M. Guillen, Equations of motion from Cederwall’s pure spinor superspace actions, JHEP 08 (2018) 033 [arXiv:1804.06979] [INSPIRE].
M. Cederwall, U. Gran, B.E.W. Nilsson and D. Tsimpis, Supersymmetric corrections to eleven-dimensional supergravity, JHEP 05 (2005) 052 [hep-th/0409107] [INSPIRE].
Y. Hyakutake and S. Ogushi, Higher derivative corrections to eleven dimensional supergravity via local supersymmetry, JHEP 02 (2006) 068 [hep-th/0601092] [INSPIRE].
N. Marcus, A. Sagnotti and W. Siegel, Ten-dimensional Supersymmetric Yang-Mills Theory in Terms of Four-dimensional Superfields, Nucl. Phys. B 224 (1983) 159 [INSPIRE].
K. Becker, M. Becker, W.D. Linch and D. Robbins, Abelian tensor hierarchy in 4D, N = 1 superspace, JHEP 03 (2016) 052 [arXiv:1601.03066] [INSPIRE].
K. Becker, M. Becker, W.D. Linch and D. Robbins, Chern-Simons actions and their gaugings in 4D, N = 1 superspace, JHEP 06 (2016) 097 [arXiv:1603.07362] [INSPIRE].
K. Becker, M. Becker, S. Guha, W.D. Linch and D. Robbins, M-theory potential from the G2 Hitchin functional in superspace, JHEP 12 (2016) 085 [arXiv:1611.03098] [INSPIRE].
K. Becker, M. Becker, D. Butter, S. Guha, W.D. Linch and D. Robbins, Eleven-dimensional supergravity in 4D, N = 1 superspace, JHEP 11 (2017) 199 [arXiv:1709.07024] [INSPIRE].
K. Becker, M. Becker, D. Butter and W.D. Linch, N = 1 supercurrents of eleven-dimensional supergravity, JHEP 05 (2018) 128 [arXiv:1803.00050] [INSPIRE].
K. Becker and D. Butter, 4D N = 1 Kaluza-Klein superspace, JHEP 09 (2020) 091 [arXiv:2003.01790] [INSPIRE].
K. Becker, D. Butter, W.D. Linch and A. Sengupta, Components of eleven-dimensional supergravity with four off-shell supersymmetries, JHEP 07 (2021) 032 [arXiv:2101.11671] [INSPIRE].
L. Brink and P.S. Howe, Eleven-Dimensional Supergravity on the Mass-Shell in Superspace, Phys. Lett. B 91 (1980) 384 [INSPIRE].
E. Cremmer and S. Ferrara, Formulation of Eleven-Dimensional Supergravity in Superspace, Phys. Lett. B 91 (1980) 61 [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton, U.S.A. (1992).
S.J. Gates, Jr. and W. Siegel, (3/2, 1) Superfield of O(2) Supergravity, Nucl. Phys. B 164 (1980) 484 [INSPIRE].
P. Binetruy, G. Girardi and R. Grimm, Supergravity couplings: A Geometric formulation, Phys. Rept. 343 (2001) 255 [hep-th/0005225] [INSPIRE].
A. Van Proeyen, Tools for supersymmetry, Ann. U. Craiova Phys. 9 (1999) 1 [hep-th/9910030] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory. II. E7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [INSPIRE].
H. Godazgar, M. Godazgar, O. Hohm, H. Nicolai and H. Samtleben, Supersymmetric E7(7) Exceptional Field Theory, JHEP 09 (2014) 044 [arXiv:1406.3235] [INSPIRE].
D. Butter, H. Samtleben and E. Sezgin, E7(7) Exceptional Field Theory in Superspace, JHEP 01 (2019) 087 [arXiv:1811.00038] [INSPIRE].
A. Ashmore, C. Strickland-Constable, D. Tennyson and D. Waldram, Generalising G2 geometry: involutivity, moment maps and moduli, JHEP 01 (2021) 158 [arXiv:1910.04795] [INSPIRE].
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Becker, K., Butter, D. & Sengupta, A. Linearized off-shell 4+7 supergeometry of 11D supergravity. J. High Energ. Phys. 2022, 127 (2022). https://doi.org/10.1007/JHEP11(2022)127
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DOI: https://doi.org/10.1007/JHEP11(2022)127