Abstract
Motivated by a recently found class of AdS7 solutions, we classify AdS5 solutions in massive IIA, finding infinitely many new analytical examples. We reduce the general problem to a set of PDEs, determining the local internal metric, which is a fibration over a surface. Under a certain simplifying assumption, we are then able to analytically solve the PDEs and give a complete list of all solutions. Among these, one class is new and regular. These spaces can be related to the AdS7 solutions via a simple universal map for the metric, dilaton and fluxes. The natural interpretation of this map is that the dual CFT6 and CFT4 are related by twisted compactification on a Riemann surface Σ g . The ratio of their free energy coefficients is proportional to the Euler characteristic of Σ g . As a byproduct, we also find the analytic expression for the AdS7 solutions, which were previously known only numerically. We determine the free energy for simple examples: it is a simple cubic function of the flux integers.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
K. Pilch and N.P. Warner, A new supersymmetric compactification of chiral IIB supergravity, Phys. Lett. B 487 (2000) 22 [hep-th/0002192] [INSPIRE].
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].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
D. Gaiotto and J. Maldacena, The Gravity duals of \( \mathcal{N}=2 \) superconformal field theories, JHEP 10 (2012) 189 [arXiv:0904.4466] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, Four-Dimensional SCFTs from M5-Branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [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].
J. Blaback, U.H. Danielsson, D. Junghans, T. Van Riet, T. Wrase and M. Zagermann, The problematic backreaction of SUSY-breaking branes, JHEP 08 (2011) 105 [arXiv:1105.4879] [INSPIRE].
F.F. Gautason, D. Junghans and M. Zagermann, Cosmological Constant, Near Brane Behavior and Singularities, JHEP 09 (2013) 123 [arXiv:1301.5647] [INSPIRE].
J. Blaback, U.H. Danielsson, D. Junghans, T. Van Riet, T. Wrase and M. Zagermann, (Anti-)Brane backreaction beyond perturbation theory, JHEP 02 (2012) 025 [arXiv:1111.2605] [INSPIRE].
D. Junghans, D. Schmidt and M. Zagermann, Curvature-induced Resolution of Anti-brane Singularities, JHEP 1410 (2014) 34 [arXiv:1402.6040] [INSPIRE].
D. Gaiotto and A. Tomasiello, Holography for (1, 0) theories in six dimensions, JHEP 12 (2014) 003 [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].
K.A. Intriligator, RG fixed points in six-dimensions via branes at orbifold singularities, Nucl. Phys. B 496 (1997) 177 [hep-th/9702038] [INSPIRE].
K.A. Intriligator, New string theories in six-dimensions via branes at orbifold singularities, Adv. Theor. Math. Phys. 1 (1998) 271 [hep-th/9708117] [INSPIRE].
J.J. Heckman, D.R. Morrison and C. Vafa, On the Classification of 6D SCFTs and Generalized ADE Orbifolds, JHEP 05 (2014) 028 [arXiv:1312.5746] [INSPIRE].
M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d Conformal Matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
A. Rota and A. Tomasiello, AdS 4 compactifications of AdS 7 solutions in type-II supergravity, arXiv:1502.06622 [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [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].
M. Gabella, J.P. Gauntlett, E. Palti, J. Sparks and D. Waldram, AdS 5 Solutions of Type IIB Supergravity and Generalized Complex Geometry, Commun. Math. Phys. 299 (2010) 365 [arXiv:0906.4109] [INSPIRE].
M.T. Anderson, C. Beem, N. Bobev and L. Rastelli, Holographic Uniformization, Commun. Math. Phys. 318 (2013) 429 [arXiv:1109.3724] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, AdS/CFT Dual Pairs from M5-Branes on Riemann Surfaces, Phys. Rev. D 85 (2012) 121901 [arXiv:1112.5487] [INSPIRE].
G. Itsios, C. Núñez, K. Sfetsos and D.C. Thompson, On Non-Abelian T-duality and new \( \mathcal{N}=1 \) backgrounds, Phys. Lett. B 721 (2013) 342 [arXiv:1212.4840] [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
O. Aharony, L. Berdichevsky and M. Berkooz, 4d \( \mathcal{N}=2 \) superconformal linear quivers with type IIA duals, JHEP 08 (2012) 131 [arXiv:1206.5916] [INSPIRE].
D. Gaiotto, \( \mathcal{N}=2 \) dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
A. Tomasiello, Reformulating supersymmetry with a generalized Dolbeault operator, JHEP 02 (2008) 010 [arXiv:0704.2613] [INSPIRE].
D. Lüst and D. Tsimpis, Supersymmetric AdS 4 compactifications of IIA supergravity, JHEP 02 (2005) 027 [hep-th/0412250] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [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].
K. Sfetsos and D.C. Thompson, New \( \mathcal{N}=1 \) supersymmetric AdS 5 backgrounds in Type IIA supergravity, JHEP 11 (2014) 006 [arXiv:1408.6545] [INSPIRE].
R.A. Reid-Edwards and B. Stefanski Jr., On Type IIA geometries dual to \( \mathcal{N}=2 \) SCFTs, Nucl. Phys. B 849 (2011) 549 [arXiv:1011.0216] [INSPIRE].
I. Bah, Quarter-BPS AdS 5 solutions in M-theory with a T 2 bundle over a Riemann surface, JHEP 08 (2013) 137 [arXiv:1304.4954] [INSPIRE].
I. Bah, AdS 5 solutions from M5-branes on Riemann surface and D6-branes sources, arXiv:1501.06072 [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: 1502.06620
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. Supersymmetric AdS5 solutions of massive IIA supergravity. J. High Energ. Phys. 2015, 195 (2015). https://doi.org/10.1007/JHEP06(2015)195
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2015)195