Abstract
Gravitational domain wall solutions in gauged supergravity are often constructed within truncations that do not include vectors. As a consequence the gauge group is only a global symmetry of this truncation. The consistency of the truncation requires the restriction to solutions with vanishing Noether charge under this global symmetry, since otherwise vector fields are sourced. We show that this has interesting consequences for the orbit structure of the solutions under the global symmetries. We investigate this for CSO(p, q, r)-gaugings in various dimensions with scalar fields truncated to the \( \mathrm{S}\mathrm{L}\left(n,\mathbb{R}\right)/\mathrm{SO}(n) \) subcoset. We prove that the seed solution — which generates all other solutions using only global transformations — has a diagonal coset matrix. This means that there exists a transformation at the boundary of the geometry that diagonalises the coset matrix and that this same transformation also diagonalises the whole flow as a consequence of the vanishing charge.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge, U.K. (2012).
C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
P. Breitenlohner, D. Maison and G.W. Gibbons, Four-Dimensional Black Holes from Kaluza-Klein Theories, Commun. Math. Phys. 120 (1988) 295 [INSPIRE].
M. Bertolini, P. Fré and M. Trigiante, The generating solution of regular N = 8 BPS black holes, Class. Quant. Grav. 16 (1999) 2987 [hep-th/9905143] [INSPIRE].
M. Trigiante, Gauged Supergravities, Phys. Rept. 680 (2017) 1 [arXiv:1609.09745] [INSPIRE].
D. Roest, M-theory and gauged supergravities, Fortsch. Phys. 53 (2005) 119 [hep-th/0408175] [INSPIRE].
M. Cvetič, S.S. Gubser, H. Lü and C.N. Pope, Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories, Phys. Rev. D 62 (2000) 086003 [hep-th/9909121] [INSPIRE].
C.M. Hull and N.P. Warner, Noncompact Gaugings From Higher Dimensions, Class. Quant. Grav. 5 (1988) 1517 [INSPIRE].
E. Bergshoeff, M. Nielsen and D. Roest, The domain walls of gauged maximal supergravities and their M-theory origin, JHEP 07 (2004) 006 [hep-th/0404100] [INSPIRE].
M. Cvetič, H. Lü and C.N. Pope, Consistent sphere reductions and universality of the Coulomb branch in the domain wall/QFT correspondence, Nucl. Phys. B 590 (2000) 213 [hep-th/0004201] [INSPIRE].
N. Alonso Alberca, E. Bergshoeff, U. Gran, R. Linares, T. Ortín and D. Roest, Domain walls of D = 8 gauged supergravities and their D = 11 origin, JHEP 06 (2003) 038 [hep-th/0303113] [INSPIRE].
P. Fré, V. Gili, F. Gargiulo, A.S. Sorin, K. Rulik and M. Trigiante, Cosmological backgrounds of superstring theory and solvable algebras: Oxidation and branes, Nucl. Phys. B 685 (2004) 3 [hep-th/0309237] [INSPIRE].
W. Chemissany, J. Rosseel, M. Trigiante and T. Van Riet, The full integration of black hole solutions to symmetric supergravity theories, Nucl. Phys. B 830 (2010) 391 [arXiv:0903.2777] [INSPIRE].
W. Chemissany, P. Fré and A.S. Sorin, The Integration Algorithm of Lax equation for both Generic Lax matrices and Generic Initial Conditions, Nucl. Phys. B 833 (2010) 220 [arXiv:0904.0801] [INSPIRE].
D.Z. Djoković, J. Patera, P. Winternitz and H. Zassenhaus, Normal forms of elements of classical real and complex Lie and Jordan algebras, J. Math. Phys. 24 (1983) 1363.
E. Bergshoeff, W. Chemissany, A. Ploegh, M. Trigiante and T. Van Riet, Generating Geodesic Flows and Supergravity Solutions, Nucl. Phys. B 812 (2009) 343 [arXiv:0806.2310] [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].
A. Guarino, CSO c superpotentials, Nucl. Phys. B 900 (2015) 501 [arXiv:1508.05055] [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: 1704.06534
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
Dorronsoro, J.D., Erbin, H. & Van Riet, T. Domain wall seeds in CSO-gauged supergravity. J. High Energ. Phys. 2017, 97 (2017). https://doi.org/10.1007/JHEP06(2017)097
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2017)097