Journal of High Energy Physics

, 2019:113 | Cite as

Classifying solutions to Romans supergravity with a zero B-field

  • Carolina Matté GreogryEmail author
Open Access
Regular Article - Theoretical Physics


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.


AdS-CFT Correspondence Supergravity Models Gauge-gravity correspondence Supersymmetry and Duality 


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


  1. [1]
    L.F. Alday, M. Fluder, C.M. Gregory, P. Richmond and J. Sparks, Supersymmetric gauge theories on squashed five-spheres and their gravity duals, JHEP 09 (2014) 067 [arXiv:1405.7194] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    L.F. Alday, M. Fluder, C.M. Gregory, P. Richmond and J. Sparks, Supersymmetric solutions to Euclidean Romans supergravity, JHEP 02 (2016) 100 [arXiv:1505.04641] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    L.J. Romans, The F(4) Gauged Supergravity in Six-dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].
  4. [4]
    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].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    J. Hong, J.T. Liu and D.R. Mayerson, Gauged Six-Dimensional Supergravity from Warped IIB Reductions, JHEP 09 (2018) 140 [arXiv:1808.04301] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    E. Malek, H. Samtleben and V. Vall Camell, Supersymmetric AdS 7 and AdS 6 vacua and their minimal consistent truncations from exceptional field theory, Phys. Lett. B 786 (2018) 171 [arXiv:1808.05597] [INSPIRE].
  7. [7]
    Y. Imamura, Supersymmetric theories on squashed five-sphere, PTEP 2013 (2013) 013B04 [arXiv:1209.0561] [INSPIRE].
  8. [8]
    L.F. Alday, P. Benetti Genolini, M. Fluder, P. Richmond and J. Sparks, Supersymmetric gauge theories on five-manifolds, JHEP 08 (2015) 007 [arXiv:1503.09090] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    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].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    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].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    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].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    J.P. Gauntlett and S. Pakis, The Geometry of D = 11 Killing spinors, JHEP 04 (2003) 039 [hep-th/0212008] [INSPIRE].
  13. [13]
    J.P. Gauntlett, D. Martelli and D. Waldram, Superstrings with intrinsic torsion, Phys. Rev. D 69 (2004) 086002 [hep-th/0302158] [INSPIRE].
  14. [14]
    P. Kaste, R. Minasian and A. Tomasiello, Supersymmetric M-theory compactifications with fluxes on seven-manifolds and G structures, JHEP 07 (2003) 004 [hep-th/0303127] [INSPIRE].
  15. [15]
    D. Martelli and J. Sparks, G structures, uxes and calibrations in M-theory, Phys. Rev. D 68 (2003) 085014 [hep-th/0306225] [INSPIRE].
  16. [16]
    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].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    J.P. Gauntlett, J.B. Gutowski and S. Pakis, The Geometry of D = 11 null Killing spinors, JHEP 12 (2003) 049 [hep-th/0311112] [INSPIRE].
  18. [18]
    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].
  19. [19]
    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].
  20. [20]
    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].
  21. [21]
    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].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5 solutions of M-theory, Class. Quant. Grav. 21 (2004) 4335 [hep-th/0402153] [INSPIRE].
  23. [23]
    L.F. Alday, P. Richmond and J. Sparks, The holographic supersymmetric Renyi entropy in five dimensions, JHEP 02 (2015) 102 [arXiv:1410.0899] [INSPIRE].
  24. [24]
    S.I. Goldberg, Integrability of almost Kähler manifolds, Proc. Am. Math. Soc. 21 (1969) 96.Google Scholar
  25. [25]
    V. Apostolov, T. Draghici and A. Moroianu, The holographic supersymmetric Renyi entropy in five dimensions, Int. J. Math. 12 (2001) 769 [math/0007122].MathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade de BrasíliaBrasíliaBrasil

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