Abstract
Expanding on previous papers, we continue studying Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. Using a set of differential constraints on a SU(2) structure, we look for further geometric solutions to such equations when we turn off the two-form potential B. We find that the six-dimensional space is described by a two-dimensional fibration over a four-dimensional manifold with a Kähler metric. We then classify these types of solutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L.F. Alday, M. Fluder, C.M. Gregory, P. Richmond and J. Sparks, Supersymmetric gauge theories on squashed five-spheres and their gravity duals, JHEP09 (2014) 067 [arXiv:1405.7194] [INSPIRE].
L.F. Alday, M. Fluder, C.M. Gregory, P. Richmond and J. Sparks, Supersymmetric solutions to Euclidean Romans supergravity, JHEP02 (2016) 100 [arXiv:1505.04641] [INSPIRE].
L.J. Romans, The F(4) Gauged Supergravity in Six-dimensions, Nucl. Phys.B 269 (1986) 691 [INSPIRE].
M. Cvetič, H. Lü and C.N. Pope, Gauged six-dimensional supergravity from massive type IIA, Phys. Rev. Lett.83 (1999) 5226 [hep-th/9906221] [INSPIRE].
J. Hong, J.T. Liu and D.R. Mayerson, Gauged Six-Dimensional Supergravity from Warped IIB Reductions, JHEP09 (2018) 140 [arXiv:1808.04301] [INSPIRE].
E. Malek, H. Samtleben and V. Vall Camell, Supersymmetric AdS 7and AdS 6vacua and their minimal consistent truncations from exceptional field theory, Phys. Lett.B 786 (2018) 171 [arXiv:1808.05597] [INSPIRE].
Y. Imamura, Supersymmetric theories on squashed five-sphere, PTEP2013 (2013) 013B04 [arXiv:1209.0561] [INSPIRE].
L.F. Alday, P. Benetti Genolini, M. Fluder, P. Richmond and J. Sparks, Supersymmetric gauge theories on five-manifolds, JHEP08 (2015) 007 [arXiv:1503.09090] [INSPIRE].
J.P. Gauntlett, D. Martelli, S. Pakis and D. Waldram, G structures and wrapped NS5-branes, Commun. Math. Phys.247 (2004) 421 [hep-th/0205050] [INSPIRE].
S. Gurrieri, J. Louis, A. Micu and D. Waldram, Mirror symmetry in generalized Calabi-Yau compactifications, Nucl. Phys.B 654 (2003) 61 [hep-th/0211102] [INSPIRE].
G. Lopes Cardoso, G. Curio, G. Dall’Agata, D. Lüst, P. Manousselis and G. Zoupanos, NonKähler string backgrounds and their five torsion classes, Nucl. Phys.B 652 (2003) 5 [hep-th/0211118] [INSPIRE].
J.P. Gauntlett and S. Pakis, The Geometry of D = 11 Killing spinors, JHEP04 (2003) 039 [hep-th/0212008] [INSPIRE].
J.P. Gauntlett, D. Martelli and D. Waldram, Superstrings with intrinsic torsion, Phys. Rev.D 69 (2004) 086002 [hep-th/0302158] [INSPIRE].
P. Kaste, R. Minasian and A. Tomasiello, Supersymmetric M-theory compactifications with fluxes on seven-manifolds and G structures, JHEP07 (2003) 004 [hep-th/0303127] [INSPIRE].
D. Martelli and J. Sparks, G structures, uxes and calibrations in M-theory, Phys. Rev.D 68 (2003) 085014 [hep-th/0306225] [INSPIRE].
K. Behrndt and M. Cvetič, Supersymmetric intersecting D6-branes and fluxes in massive type IIA string theory, Nucl. Phys.B 676 (2004) 149 [hep-th/0308045] [INSPIRE].
J.P. Gauntlett, J.B. Gutowski and S. Pakis, The Geometry of D = 11 null Killing spinors, JHEP12 (2003) 049 [hep-th/0311112] [INSPIRE].
K. Behrndt and C. Jeschek, Fluxes in M-theory on seven manifolds: G structures and superpotential, Nucl. Phys.B 694 (2004) 99 [hep-th/0311119] [INSPIRE].
S. Fidanza, R. Minasian and A. Tomasiello, Mirror symmetric SU(3) structure manifolds with NS fluxes, Commun. Math. Phys.254 (2005) 401 [hep-th/0311122] [INSPIRE].
G. Dall'Agata and N. Prezas, N = 1 geometries for M-theory and type IIA strings with fluxes, Phys. Rev.D 69 (2004) 066004 [hep-th/0311146] [INSPIRE].
J.P. Gauntlett, J.B. Gutowski, C.M. Hull, S. Pakis and H.S. Reall, All supersymmetric solutions of minimal supergravity in five-dimensions, Class. Quant. Grav.20 (2003) 4587 [hep-th/0209114] [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5solutions of M-theory, Class. Quant. Grav.21 (2004) 4335 [hep-th/0402153] [INSPIRE].
L.F. Alday, P. Richmond and J. Sparks, The holographic supersymmetric Renyi entropy in five dimensions, JHEP02 (2015) 102 [arXiv:1410.0899] [INSPIRE].
S.I. Goldberg, Integrability of almost Kähler manifolds, Proc. Am. Math. Soc.21 (1969) 96.
V. Apostolov, T. Draghici and A. Moroianu, The holographic supersymmetric Renyi entropy in five dimensions, Int. J. Math.12 (2001) 769 [math/0007122].
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: 1906.01660
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Gregory, C.M. Classifying solutions to Romans supergravity with a zero B-field. J. High Energ. Phys. 2019, 113 (2019). https://doi.org/10.1007/JHEP09(2019)113
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2019)113