Abstract
Very few AdS6 × M 4 supersymmetric solutions are known: one in massive IIA, and two IIB solutions dual to it. The IIA solution is known to be unique; in this paper, we use the pure spinor approach to give a classification for IIB supergravity. We reduce the problem to two PDEs on a two-dimensional space Σ. M 4 is then a fibration of S 2 over Σ; the metric and fluxes are completely determined in terms of the solution to the PDEs. The results seem likely to accommodate near-horizon limits of (p, q)-fivebrane webs studied in the literature as a source of CFT5’s. We also show that there are no AdS6 solutions in eleven-dimensional supergravity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Change history
04 May 2015
An Erratum to this paper has been published: https://doi.org/10.1007/JHEP05(2015)012
References
N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388 (1996) 753 [hep-th/9608111] [INSPIRE].
D.R. Morrison and N. Seiberg, Extremal transitions and five-dimensional supersymmetric field theories, Nucl. Phys. B 483 (1997) 229 [hep-th/9609070] [INSPIRE].
K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [INSPIRE].
O. Aharony and A. Hanany, Branes, superpotentials and superconformal fixed points, Nucl. Phys. B 504 (1997) 239 [hep-th/9704170] [INSPIRE].
O. DeWolfe, A. Hanany, A. Iqbal and E. Katz, Five-branes, seven-branes and five-dimensional E n field theories, JHEP 03 (1999) 006 [hep-th/9902179] [INSPIRE].
N.C. Leung and C. Vafa, Branes and toric geometry, Adv. Theor. Math. Phys. 2 (1998) 91 [hep-th/9711013] [INSPIRE].
F. Benini, S. Benvenuti and Y. Tachikawa, Webs of five-branes and \( \mathcal{N}=2 \) superconformal field theories, JHEP 09 (2009) 052 [arXiv:0906.0359] [INSPIRE].
D. Gaiotto, \( \mathcal{N}=2 \) dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
O. Lunin, Brane webs and 1/4-BPS geometries, JHEP 09 (2008) 028 [arXiv:0802.0735] [INSPIRE].
D. Youm, Localized intersecting BPS branes, hep-th/9902208 [INSPIRE].
A. Brandhuber and Y. Oz, The D4-D8 brane system and five-dimensional fixed points, Phys. Lett. B 460 (1999) 307 [hep-th/9905148] [INSPIRE].
S. Ferrara, A. Kehagias, H. Partouche and A. Zaffaroni, AdS 6 interpretation of 5D superconformal field theories, Phys. Lett. B 431 (1998) 57 [hep-th/9804006] [INSPIRE].
L.J. Romans, The F(4) gauged supergravity in six-dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].
O. Bergman and D. Rodriguez-Gomez, 5D quivers and their AdS 6 duals, JHEP 07 (2012) 171 [arXiv:1206.3503] [INSPIRE].
M. Cvetič, H. Lü, C.N. Pope and J.F. Vazquez-Poritz, AdS in warped space-times, Phys. Rev. D 62 (2000) 122003 [hep-th/0005246] [INSPIRE].
Y. Lozano, E. Ó Colgáin, D. Rodríguez-Gómez and K. Sfetsos, Supersymmetric AdS6 via T duality, Phys. Rev. Lett. 110 (2013) 231601 [arXiv:1212.1043] [INSPIRE].
K. Sfetsos and D.C. Thompson, On non-abelian T-dual geometries with Ramond fluxes, Nucl. Phys. B 846 (2011) 21 [arXiv:1012.1320] [INSPIRE].
Y. Lozano, E. O Colgain, K. Sfetsos and D.C. Thompson, Non-abelian T-duality, Ramond fields and coset geometries, JHEP 06 (2011) 106 [arXiv:1104.5196] [INSPIRE].
Y. Lozano, E.O. Colgain and D. Rodriguez-Gomez, Hints of 5D fixed point theories from non-abelian T-duality, arXiv:1311.4842 [INSPIRE].
F. Apruzzi, M. Fazzi, D. Rosa and A. Tomasiello, All AdS 7 solutions of type-II supergravity, JHEP 04 (2014) 064 [arXiv:1309.2949] [INSPIRE].
N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser. 54 (2003) 281 [math/0209099] [INSPIRE].
M. Gualtieri, Generalized complex geometry, Ph.D. thesis, Advisor N. Hitchin, Oxford University, Oxford U.K. (2003) [math.DG/0401221] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and A. Tomasiello, Generalized structures of \( \mathcal{N}=1 \) vacua, JHEP 11 (2005) 020 [hep-th/0505212] [INSPIRE].
A. Tomasiello, Generalized structures of ten-dimensional supersymmetric solutions, JHEP 03 (2012) 073 [arXiv:1109.2603] [INSPIRE].
A. Passias, A note on supersymmetric AdS 6 solutions of massive type IIA supergravity, JHEP 01 (2013) 113 [arXiv:1209.3267] [INSPIRE].
R.L. Bryant, P. Griffiths, S. Chern, R.B. Gardner and H.L. Goldschmidt, Exterior differential systems, Springer, Germany (1991).
H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers and E. Herlt, Exact solutions of Einstein’s field equations, Cambridge University Press, Cambridge U.K. (2003).
D. Gaiotto and A. Tomasiello, Holography for (1,0) theories in six dimensions, arXiv:1404.0711 [INSPIRE].
A. Hanany and A. Zaffaroni, Branes and six-dimensional supersymmetric theories, Nucl. Phys. B 529 (1998) 180 [hep-th/9712145] [INSPIRE].
I. Brunner and A. Karch, Branes at orbifolds versus Hanany Witten in six-dimensions, JHEP 03 (1998) 003 [hep-th/9712143] [INSPIRE].
D. Lüst, P. Patalong and D. Tsimpis, Generalized geometry, calibrations and supersymmetry in diverse dimensions, JHEP 01 (2011) 063 [arXiv:1010.5789] [INSPIRE].
D. Prins and D. Tsimpis, IIB supergravity on manifolds with SU(4) structure and generalized geometry, JHEP 07 (2013) 180 [arXiv:1306.2543] [INSPIRE].
D. Rosa, Generalized geometry of two-dimensional vacua, JHEP 07 (2014) 111 [arXiv:1310.6357] [INSPIRE].
D. Prins and D. Tsimpis, IIA supergravity and M-theory on manifolds with SU(4) structure, Phys. Rev. D 89 (2014) 064030 [arXiv:1312.1692] [INSPIRE].
P. Koerber and L. Martucci, D-branes on AdS flux compactifications, JHEP 01 (2008) 047 [arXiv:0710.5530] [INSPIRE].
D. Rosa and A. Tomasiello, Pure spinor equations to lift gauged supergravity, JHEP 01 (2014) 176 [arXiv:1305.5255] [INSPIRE].
D. Lüst and D. Tsimpis, Supersymmetric AdS 4 compactifications of IIA supergravity, JHEP 02 (2005) 027 [hep-th/0412250] [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5 solutions of type IIB supergravity, Class. Quant. Grav. 23 (2006) 4693 [hep-th/0510125] [INSPIRE].
P. Koerber and D. Tsimpis, Supersymmetric sources, integrability and generalized-structure compactifications, JHEP 08 (2007) 082 [arXiv:0706.1244] [INSPIRE].
N. Halmagyi and A. Tomasiello, Generalized Kähler potentials from supergravity, Commun. Math. Phys. 291 (2009) 1 [arXiv:0708.1032] [INSPIRE].
D. Tong, NS5-branes, T duality and world sheet instantons, JHEP 07 (2002) 013 [hep-th/0204186] [INSPIRE].
A. Sen, F theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
R.L. Bryant, Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor, math.DG/0004073.
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: 1406.0852
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
Apruzzi, F., Fazzi, M., Passias, A. et al. AdS6 solutions of type II supergravity. J. High Energ. Phys. 2014, 99 (2014). https://doi.org/10.1007/JHEP11(2014)099
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2014)099