Abstract
We describe how one may use either the superPoincaré algebra or the exceptional algebra to construct maximal supergravity theories in the light-cone formalism. The d = 4 construction shows both symmetries albeit in a non-linearly realized manner. In d = 11, we find that we have to choose which of these two symmetries to use, in constructing the theory. In order to understand the other “unused” symmetry, one has to perform a highly non-trivial field redefinition. We argue that this shows that one cannot trust counterterm arguments that do not take the full symmetry of the theory into account. Finally we discuss possible consequences for Superstring theory and M-theory.
Article PDF
Similar content being viewed by others
References
E. Cremmer and B. Julia, The SO(8) Supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
E. Cremmer, B. Julia and J. Scherk, Supergravity Theory in Eleven-Dimensions, Phys. Lett. B 76 (1978) 409 [INSPIRE].
L. Brink and P.S. Howe, The N = 8 Supergravity in Superspace, Phys. Lett. B 88 (1979) 268 [INSPIRE].
P.S. Howe and U. Lindström, Higher Order Invariants in Extended Supergravity, Nucl. Phys. B 181 (1981) 487 [INSPIRE].
Z. Bern, J.J. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, Amplitudes and Ultraviolet Behavior of N = 8 Supergravity, Fortsch. Phys. 59 (2011) 561 [arXiv:1103.1848] [INSPIRE].
A.K.H. Bengtsson, I. Bengtsson and L. Brink, Cubic Interaction Terms for Arbitrarily Extended Supermultiplets, Nucl. Phys. B 227 (1983) 41 [INSPIRE].
S. Ananth, L. Brink, R. Heise and H.G. Svendsen, The N = 8 Supergravity Hamiltonian as a Quadratic Form, Nucl. Phys. B 753 (2006) 195 [hep-th/0607019] [INSPIRE].
L. Brink, S.-S. Kim and P. Ramond, E 7(7) on the Light Cone, JHEP 06 (2008) 034 [arXiv:0801.2993] [INSPIRE].
L. Brink, O. Lindgren and B.E.W. Nilsson, N = 4 Yang-Mills Theory on the Light Cone, Nucl. Phys. B 212 (1983) 401 [INSPIRE].
S. Ananth, L. Brink and P. Ramond, Eleven-dimensional supergravity in light-cone superspace, JHEP 05 (2005) 003 [hep-th/0501079] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory. II. E 7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, \( {E_d}_{(d)}\times {\mathbb{R}}^{+} \) generalised geometry, connections and M-theory, JHEP 02 (2014) 054 [arXiv:1112.3989] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Generalised geometry from the ground up, JHEP 02 (2014) 075 [arXiv:1307.8295] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Einstein-Cartan Calculus for Exceptional Geometry, JHEP 06 (2014) 021 [arXiv:1401.5984] [INSPIRE].
B. de Wit and H. Nicolai, Hidden Symmetry in d = 11 Supergravity, Phys. Lett. B 155 (1985) 47 [INSPIRE].
B. de Wit and H. Nicolai, d = 11 Supergravity With Local SU(8) Invariance, Nucl. Phys. B 274 (1986) 363 [INSPIRE].
N. Marcus and J.H. Schwarz, Three-Dimensional Supergravity Theories, Nucl. Phys. B 228 (1983) 145 [INSPIRE].
H. Nicolai, D = 11 Supergravity With Local SO(16) Invariance, Phys. Lett. B 187 (1987) 316 [INSPIRE].
L. Brink, S.-S. Kim and P. Ramond, E 8(8) in Light Cone Superspace, JHEP 07 (2008) 113 [arXiv:0804.4300] [INSPIRE].
A.K.H. Bengtsson, L. Brink and S.-S. Kim, Counterterms in Gravity in the Light-Front Formulation and a D = 2 Conformal-like Symmetry in Gravity, JHEP 03 (2013) 118 [arXiv:1212.2776] [INSPIRE].
G. Bossard and H. Nicolai, Counterterms vs. Dualities, JHEP 08 (2011) 074 [arXiv:1105.1273] [INSPIRE].
S. Ananth, L. Brink and P. Ramond, Oxidizing super Yang-Mills from (N = 4, d = 4) to (N = 1, d = 10), JHEP 07 (2004) 082 [hep-th/0405150] [INSPIRE].
B. Julia, Kac-Moody Symmetry Of Gravitation And Supergravity Theories, LPTENS-82-22 C82-07-06 [INSPIRE].
P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [INSPIRE].
T. Damour, M. Henneaux and H. Nicolai, E 10 and a ‘small tension expansion’ of M-theory, Phys. Rev. Lett. 89 (2002) 221601 [hep-th/0207267] [INSPIRE].
T. Damour, A. Kleinschmidt and H. Nicolai, Hidden symmetries and the fermionic sector of eleven-dimensional supergravity, Phys. Lett. B 634 (2006) 319 [hep-th/0512163] [INSPIRE].
L. Brink, P. Di Vecchia and P.S. Howe, A Locally Supersymmetric and Reparametrization Invariant Action for the Spinning String, Phys. Lett. B 65 (1976) 471 [INSPIRE].
S. Deser and B. Zumino, A Complete Action for the Spinning String, Phys. Lett. B 65 (1976) 369 [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: 1601.02836
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
Ananth, S., Brink, L. & Majumdar, S. Exceptional versus superPoincaré algebra as the defining symmetry of maximal supergravity. J. High Energ. Phys. 2016, 51 (2016). https://doi.org/10.1007/JHEP03(2016)051
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2016)051