Abstract
We perform a detailed analysis of the vacua of ω-deformed SO(8) supergravity in four dimensions. In particular, using Tensorflow-based numerical methods, we track how the equilibria of the theory change when varying the electric-magnetic deformation parameter ω. Apart from describing various properties of different equilibria (390 in total), we show that as ω is deformed, the SO(3), \( \mathcal{N} \) = 1 vacuum of the de Wit-Nicolai theory becomes equivalent to a critical point in U(4) ⋉ ℝ12 gauged supergravity with a known uplift in IIB supergravity. The procedure employed here to obtain a new gauging with a guaranteed equilibrium is generic and allows one to obtain further admissible noncompact gaugings via ω-deformation, all of which have guaranteed critical points, and some of which may be novel upliftable solutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. de Wit and H. Nicolai, The Consistency of the S7 Truncation in D = 11 Supergravity, Nucl. Phys. B 281 (1987) 211 [INSPIRE].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistency of the AdS7 × S4 reduction and the origin of selfduality in odd dimensions, Nucl. Phys. B 581 (2000) 179 [hep-th/9911238] [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, Fortsch. Phys. 65 (2017) 1700048 [arXiv:1401.3360] [INSPIRE].
O. Hohm and H. Samtleben, Consistent Kaluza-Klein Truncations via Exceptional Field Theory, JHEP 01 (2015) 131 [arXiv:1410.8145] [INSPIRE].
I.M. Comsa, M. Firsching and T. Fischbacher, SO(8) Supergravity and the Magic of Machine Learning, JHEP 08 (2019) 057 [arXiv:1906.00207] [INSPIRE].
C. Krishnan, V. Mohan and S. Ray, Machine Learning \( \mathcal{N} \) = 8, D = 5 Gauged Supergravity, Fortsch. Phys. 68 (2020) 2000027 [arXiv:2002.12927] [INSPIRE].
N. Bobev, T. Fischbacher, F.F. Gautason and K. Pilch, A cornucopia of AdS5 vacua, JHEP 07 (2020) 240 [arXiv:2003.03979] [INSPIRE].
N. Bobev, T. Fischbacher, F.F. Gautason and K. Pilch, New AdS4 Vacua in Dyonic ISO(7) Gauged Supergravity, arXiv:2011.08542 [INSPIRE].
T. Fischbacher, The Many vacua of gauged extended supergravities, Gen. Rel. Grav. 41 (2009) 315 [arXiv:0811.1915] [INSPIRE].
T. Fischbacher, Fourteen new stationary points in the scalar potential of SO(8)-gauged N = 8, D = 4 supergravity, JHEP 09 (2010) 068 [arXiv:0912.1636] [INSPIRE].
T. Fischbacher, Numerical tools to validate stationary points of SO(8)-gauged N = 8 D = 4 supergravity, Comput. Phys. Commun. 183 (2012) 780 [arXiv:1007.0600] [INSPIRE].
T. Fischbacher, The Encyclopedic Reference of Critical Points for SO(8)-Gauged N =8 Supergravity. Part 1: Cosmological Constants in the Range -Λ/g^2 ∈ [6 : 14.7), arXiv:1109.1424 [INSPIRE].
H. Samtleben, Lectures on Gauged Supergravity and Flux Compactifications, Class. Quant. Grav. 25 (2008) 214002 [arXiv:0808.4076] [INSPIRE].
A. Gallerati and M. Trigiante, Introductory Lectures on Extended Supergravities and Gaugings, Springer Proc. Phys. 176 (2016) 41 [arXiv:1809.10647] [INSPIRE].
M. Trigiante, Gauged Supergravities, Phys. Rept. 680 (2017) 1 [arXiv:1609.09745] [INSPIRE].
D.S. Berman and C.D.A. Blair, The Geometry, Branes and Applications of Exceptional Field Theory, Int. J. Mod. Phys. A 35 (2020) 2030014 [arXiv:2006.09777] [INSPIRE].
G. Dall’Agata, G. Inverso and M. Trigiante, Evidence for a family of SO(8) gauged supergravity theories, Phys. Rev. Lett. 109 (2012) 201301 [arXiv:1209.0760] [INSPIRE].
G. Dall’Agata, G. Inverso and A. Marrani, Symplectic Deformations of Gauged Maximal Supergravity, JHEP 07 (2014) 133 [arXiv:1405.2437] [INSPIRE].
A. Guarino, D.L. Jafferis and O. Varela, String Theory Origin of Dyonic N = 8 Supergravity and Its Chern-Simons Duals, Phys. Rev. Lett. 115 (2015) 091601 [arXiv:1504.08009] [INSPIRE].
A. Guarino and O. Varela, Consistent \( \mathcal{N} \) = 8 truncation of massive IIA on S6, JHEP 12 (2015) 020 [arXiv:1509.02526] [INSPIRE].
G. Inverso, H. Samtleben and M. Trigiante, Type II supergravity origin of dyonic gaugings, Phys. Rev. D 95 (2017) 066020 [arXiv:1612.05123] [INSPIRE].
E. Malek and H. Samtleben, Ten-dimensional origin of Minkowski vacua in N =8 supergravity, Phys. Lett. B 776 (2018) 64 [arXiv:1710.02163] [INSPIRE].
G. Inverso, Generalised Scherk-Schwarz reductions from gauged supergravity, JHEP 12 (2017) 124 [Erratum ibid. 06 (2021) 148] [arXiv:1708.02589] [INSPIRE].
A. Borghese, A. Guarino and D. Roest, All G2 invariant critical points of maximal supergravity, JHEP 12 (2012) 108 [arXiv:1209.3003] [INSPIRE].
G. Dall’Agata and G. Inverso, de Sitter vacua in N = 8 supergravity and slow-roll conditions, Phys. Lett. B 718 (2013) 1132 [arXiv:1211.3414] [INSPIRE].
A. Borghese, A. Guarino and D. Roest, Triality, Periodicity and Stability of SO(8) Gauged Supergravity, JHEP 05 (2013) 107 [arXiv:1302.6057] [INSPIRE].
F. Catino, G. Dall’Agata, G. Inverso and F. Zwirner, On the moduli space of spontaneously broken N = 8 supergravity, JHEP 09 (2013) 040 [arXiv:1307.4389] [INSPIRE].
A. Gallerati, H. Samtleben and M. Trigiante, The \( \mathcal{N} \) > 2 supersymmetric AdS vacua in maximal supergravity, JHEP 12 (2014) 174 [arXiv:1410.0711] [INSPIRE].
B. de Wit and H. Nicolai, N = 8 Supergravity, Nucl. Phys. B 208 (1982) 323 [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, New Gaugings and Non-Geometry, Fortsch. Phys. 65 (2017) 1700049 [arXiv:1506.03457] [INSPIRE].
G. Dall’Agata and G. Inverso, On the Vacua of N = 8 Gauged Supergravity in 4 Dimensions, Nucl. Phys. B 859 (2012) 70 [arXiv:1112.3345] [INSPIRE].
A. Borghese, G. Dibitetto, A. Guarino, D. Roest and O. Varela, The SU(3)-invariant sector of new maximal supergravity, JHEP 03 (2013) 082 [arXiv:1211.5335] [INSPIRE].
T. Fischbacher and B. Scellier, to appear.
D. Berman, T. Fischbacher and G. Inverso, New \( \mathcal{N} \) = 1 AdS4 solutions of type IIB supergravity, JHEP 03 (2022) 097 [arXiv:2111.03002] [INSPIRE].
Google Colab Notebook on M-theory research, https://github.com/google-research/google-research/tree/master/m_theory/colab/so8_omega_colab.ipynb.
B. de Wit, H. Samtleben and M. Trigiante, The Maximal D = 4 supergravities, JHEP 06 (2007) 049 [arXiv:0705.2101] [INSPIRE].
B. de Wit and H. Nicolai, Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions, JHEP 05 (2013) 077 [arXiv:1302.6219] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
G. Inverso, Electric-magnetic deformations of D = 4 gauged supergravities, JHEP 03 (2016) 138 [arXiv:1512.04500] [INSPIRE].
Y. Pang, C.N. Pope and J. Rong, Holographic RG flow in a new SO(3) × SO(3) sector of ω-deformed SO(8) gauged \( \mathcal{N} \) = 8 supergravity, JHEP 08 (2015) 122 [arXiv:1506.04270] [INSPIRE].
N. Bobev, T. Fischbacher and K. Pilch, Properties of the new \( \mathcal{N} \) = 1 AdS4 vacuum of maximal supergravity, JHEP 01 (2020) 099 [arXiv:1909.10969] [INSPIRE].
G. Aldazabal, P.G. Cámara, A. Font and L.E. Ibáñez, More dual fluxes and moduli fixing, JHEP 05 (2006) 070 [hep-th/0602089] [INSPIRE].
G. Dall’Agata and N. Prezas, Scherk-Schwarz reduction of M-theory on G2-manifolds with fluxes, JHEP 10 (2005) 103 [hep-th/0509052] [INSPIRE].
T. Fischbacher, H. Nicolai and H. Samtleben, Nonsemisimple and complex gaugings of N = 16 supergravity, Commun. Math. Phys. 249 (2004) 475 [hep-th/0306276] [INSPIRE].
H. Abelson and G.J. Sussman, Structure and interpretation of computer programs, The MIT Press (1996).
N. Bobev, F.F. Gautason and J. van Muiden, Holographic 3d \( \mathcal{N} \) = 1 Conformal Manifolds, arXiv:2111.11461 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2201.04173
Supplementary Information
ESM 1
(ZIP 746 kb)
Rights and permissions
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.
About this article
Cite this article
Berman, D., Fischbacher, T., Inverso, G. et al. Vacua of ω-deformed SO(8) supergravity. J. High Energ. Phys. 2022, 133 (2022). https://doi.org/10.1007/JHEP06(2022)133
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2022)133