Abstract
We show how to use Exceptional Field Theory to compute the full Kaluza-Klein spectra of 10- and 11-dimensional supergravity around deformations of backgrounds of maximal gauged supergravity by scalar modes that do not form part of the consistent truncation. This includes deformations of AdS4 × S7 and AdS5 × S5 by modes that are not part of the \( \mathcal{N} \) = 8 supermultiplet. As an application, we compute the full Kaluza-Klein spectrum of the \( \mathcal{N} \) = 1 and \( \mathcal{N} \) = 0 squashed S7. In this example, all conformal dimensions are captured by a universal formula in terms of the Casimir operators and additional quantum numbers which organise the spectrum.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Salam and J.A. Strathdee, On Kaluza-Klein Theory, Annals Phys. 141 (1982) 316 [INSPIRE].
C. Bachas and J. Estes, Spin-2 spectrum of defect theories, JHEP 06 (2011) 005 [arXiv:1103.2800] [INSPIRE].
E. Malek and H. Samtleben, Kaluza-Klein Spectrometry for Supergravity, Phys. Rev. Lett. 124 (2020) 101601 [arXiv:1911.12640] [INSPIRE].
E. Malek and H. Samtleben, Kaluza-Klein Spectrometry from Exceptional Field Theory, Phys. Rev. D 102 (2020) 106016 [arXiv:2009.03347] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional Form of D = 11 Supergravity, Phys. Rev. Lett. 111 (2013) 231601 [arXiv:1308.1673] [INSPIRE].
E. Malek, H. Nicolai and H. Samtleben, Tachyonic Kaluza-Klein modes and the AdS swampland conjecture, JHEP 08 (2020) 159 [arXiv:2005.07713] [INSPIRE].
O. Varela, Super-Chern-Simons spectra from Exceptional Field Theory, JHEP 04 (2021) 283 [arXiv:2010.09743] [INSPIRE].
A. Guarino, E. Malek and H. Samtleben, Stable Nonsupersymmetric Anti-de Sitter Vacua of Massive IIA Supergravity, Phys. Rev. Lett. 126 (2021) 061601 [arXiv:2011.06600] [INSPIRE].
M. Cesàro and O. Varela, Kaluza-Klein fermion mass matrices from exceptional field theory and \( \mathcal{N} \) = 1 spectra, JHEP 03 (2021) 138 [arXiv:2012.05249] [INSPIRE].
N. Bobev et al., Kaluza-Klein Spectroscopy for the Leigh-Strassler SCFT, JHEP 04 (2021) 208 [arXiv:2012.07089] [INSPIRE].
A. Giambrone, E. Malek, H. Samtleben and M. Trigiante, Global properties of the conformal manifold for S-fold backgrounds, JHEP 06 (2021) 111 [arXiv:2103.10797] [INSPIRE].
M. Cesàro, G. Larios and O. Varela, Supersymmetric spectroscopy on AdS4 × S7 and AdS4 × S6, JHEP 07 (2021) 094 [arXiv:2103.13408] [INSPIRE].
M. Cesàro, G. Larios and O. Varela, The spectrum of marginally-deformed \( \mathcal{N} \) = 2 CFTs with AdS4 S-fold duals of type IIB, JHEP 12 (2021) 214 [arXiv:2109.11608] [INSPIRE].
A. Giambrone et al., Holographic evidence for nonsupersymmetric conformal manifolds, Phys. Rev. D 105 (2022) 066018 [arXiv:2112.11966] [INSPIRE].
M. Cesàro, G. Larios and O. Varela, \( \mathcal{N} \) = 1 S-fold spectroscopy, JHEP 08 (2022) 242 [arXiv:2206.04064] [INSPIRE].
H. Kim and N. Kim, On the superconformal index of Chern-Simons theories and their KK spectrometry, JHEP 10 (2021) 241 [arXiv:2108.07182] [INSPIRE].
A. Guarino and C. Sterckx, S-folds and holographic RG flows on the D3-brane, JHEP 06 (2021) 051 [arXiv:2103.12652] [INSPIRE].
M.A. Awada, M.J. Duff and C.N. Pope, N = 8 Supergravity Breaks Down to N = 1, Phys. Rev. Lett. 50 (1983) 294 [INSPIRE].
M.J. Duff, B.E.W. Nilsson and C.N. Pope, Spontaneous Supersymmetry Breaking by the Squashed Seven Sphere, Phys. Rev. Lett. 50 (1983) 2043 [Erratum ibid. 51 (1983) 846] [INSPIRE].
O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [INSPIRE].
N. Bobev, P. Bomans, F.F. Gautason and V.S. Min, Marginal deformations from type IIA supergravity, SciPost Phys. 10 (2021) 140 [arXiv:2103.02038] [INSPIRE].
N. Bobev, F.F. Gautason and J. van Muiden, Holographic 3d \( \mathcal{N} \) = 1 Conformal Manifolds, arXiv:2111.11461 [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, Fortsch. Phys. 65 (2017) 1700048 [arXiv:1401.3360] [INSPIRE].
M.J. Duff, B.E.W. Nilsson and C.N. Pope, Kaluza-Klein Supergravity, Phys. Rept. 130 (1986) 1 [INSPIRE].
B.E.W. Nilsson and C.N. Pope, Scalar and Dirac Eigenfunctions on the Squashed Seven Sphere, Phys. Lett. B 133 (1983) 67 [INSPIRE].
K. Yamagishi, Mass Spectra of Vector Particles in D = 11 Supergravity Compactified on Squashed Seven Sphere, Phys. Lett. B 137 (1984) 165 [INSPIRE].
B.E.W. Nilsson, A. Padellaro and C.N. Pope, The role of singletons in S7 compactifications, JHEP 07 (2019) 124 [arXiv:1811.06228] [INSPIRE].
S. Ekhammar and B.E.W. Nilsson, On the squashed seven-sphere operator spectrum, JHEP 12 (2021) 057 [arXiv:2105.05229] [INSPIRE].
J. Karlsson, Compactifications of String/M-Theory and the Swampland: A Study of the AdS4 Mass Spectrum of Eleven-Dimensional Supergravity on the Squashed Seven-Sphere, M.Sc. thesis, Chalmers University of Technology, Gothenburg, Sweden (2021) [arXiv:2110.09885] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory. II. E7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Ed(d) × ℝ+ generalised geometry, connections and M theory, JHEP 02 (2014) 054 [arXiv:1112.3989] [INSPIRE].
D.S. Berman, M. Cederwall, A. Kleinschmidt and D.C. Thompson, The gauge structure of generalised diffeomorphisms, JHEP 01 (2013) 064 [arXiv:1208.5884] [INSPIRE].
O. Hohm and H. Samtleben, Consistent Kaluza-Klein Truncations via Exceptional Field Theory, JHEP 01 (2015) 131 [arXiv:1410.8145] [INSPIRE].
B. de Wit, H. Samtleben and M. Trigiante, The Maximal D=4 supergravities, JHEP 06 (2007) 049 [arXiv:0705.2101] [INSPIRE].
S.S. Gubser, Einstein manifolds and conformal field theories, Phys. Rev. D 59 (1999) 025006 [hep-th/9807164] [INSPIRE].
A. Ceresole, G. Dall’Agata, R. D’Auria and S. Ferrara, Spectrum of type IIB supergravity on AdS(5) x T**11: Predictions on N=1 SCFT’s, Phys. Rev. D 61 (2000) 066001 [hep-th/9905226] [INSPIRE].
A. Ashmore, M. Petrini, E.L. Tasker and D. Waldram, Exactly Marginal Deformations and Their Supergravity Duals, Phys. Rev. Lett. 128 (2022) 191601 [arXiv:2112.08375] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional Field Theory I: E6(6) covariant Form of M-Theory and Type IIB, Phys. Rev. D 89 (2014) 066016 [arXiv:1312.0614] [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: 2212.01135
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
Duboeuf, B., Malek, E. & Samtleben, H. Kaluza-Klein spectrometry beyond consistent truncations: the squashed S7. J. High Energ. Phys. 2023, 62 (2023). https://doi.org/10.1007/JHEP04(2023)062
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2023)062