Abstract
Using exceptional field theory we construct supersymmetric warped AdS7 vacua of massive IIA and AdS6 vacua of IIB, as well as their consistent truncations including vector multiplets. We show that there are no consistent truncations of massive IIA supergravity around its supersymmetric AdS7 vacua with vector multiplets when the Romans mass is non-vanishing. For AdS6 vacua of IIB supergravity, we find that in addition to the consistent truncation to pure F(4) gauged SUGRA, the only other half-maximal truncations that are consistent result in F(4) gauged SUGRA coupled to one or two Abelian vector multiplets, to three non-Abelian vector multiplets, leading to an ISO(3) gauged SUGRA, or to three non-Abelian plus one Abelian vector multiplet, leading to an ISO(3) × U(1) gauged SUGRA. These consistent truncations with vector multiplets exist when the two holomorphic functions that define the AdS6 vacua satisfy certain differential conditions which we derive. We use these to deduce that no globally regular AdS6 solutions admit a consistent truncation to F(4) gauged SUGRA with two vector multiplets, and show that the Abelian T-dual of the Brandhuber-Oz vacuum allows a consistent truncation to F(4) gauged SUGRA with a single vector multiplet.
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J.P. Gauntlett and O. Varela, Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions, Phys. Rev. D 76 (2007) 126007 [arXiv:0707.2315] [INSPIRE].
D.S. Berman and M.J. Perry, Generalized Geometry and M-theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [INSPIRE].
D.S. Berman, H. Godazgar, M. Godazgar and M.J. Perry, The Local symmetries of M-theory and their formulation in generalised geometry, JHEP 01 (2012) 012 [arXiv:1110.3930] [INSPIRE].
D.S. Berman, M. Cederwall, A. Kleinschmidt and D.C. Thompson, The gauge structure of generalised diffeomorphisms, JHEP 01 (2013) 064 [arXiv:1208.5884] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional Form of D = 11 Supergravity, Phys. Rev. Lett. 111 (2013) 231601 [arXiv:1308.1673] [INSPIRE].
P. Pires Pacheco and D. Waldram, M-theory, exceptional generalised geometry and superpotentials, JHEP 09 (2008) 123 [arXiv:0804.1362] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, E d(d) × ℝ+ generalised geometry, connections and M-theory, JHEP 02 (2014) 054 [arXiv:1112.3989] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry II: E d(d) × ℝ+ and M-theory, JHEP 03 (2014) 019 [arXiv:1212.1586] [INSPIRE].
G. Aldazabal, W. Baron, D. Marqués and C. Núñez, The effective action of Double Field Theory, JHEP 11 (2011) 052 [Erratum ibid. 1111 (2011) 109] [arXiv:1109.0290] [INSPIRE].
D. Geissbühler, Double Field Theory and N = 4 Gauged Supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].
M. Graña and D. Marqués, Gauged Double Field Theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].
D.S. Berman, E.T. Musaev, D.C. Thompson and D.C. Thompson, Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions, JHEP 10 (2012) 174 [arXiv:1208.0020] [INSPIRE].
J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys. B 153 (1979) 61 [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, Fortsch. Phys. 65 (2017) 1700048 [arXiv:1401.3360] [INSPIRE].
O. Hohm and H. Samtleben, Consistent Kaluza-Klein Truncations via Exceptional Field Theory, JHEP 01 (2015) 131 [arXiv:1410.8145] [INSPIRE].
A. Baguet, O. Hohm and H. Samtleben, Consistent Type IIB Reductions to Maximal 5D Supergravity, Phys. Rev. D 92 (2015) 065004 [arXiv:1506.01385] [INSPIRE].
E. Malek and H. Samtleben, Dualising consistent IIA/ IIB truncations, JHEP 12 (2015) 029 [arXiv:1510.03433] [INSPIRE].
A. Baguet, C.N. Pope and H. Samtleben, Consistent Pauli reduction on group manifolds, Phys. Lett. B 752 (2016) 278 [arXiv:1510.08926] [INSPIRE].
F. Ciceri, A. Guarino and G. Inverso, The exceptional story of massive IIA supergravity, JHEP 08 (2016) 154 [arXiv:1604.08602] [INSPIRE].
D. Cassani, O. de Felice, M. Petrini, C. Strickland-Constable and D. Waldram, Exceptional generalised geometry for massive IIA and consistent reductions, JHEP 08 (2016) 074 [arXiv:1605.00563] [INSPIRE].
G. Inverso, H. Samtleben and M. Trigiante, Type II supergravity origin of dyonic gaugings, Phys. Rev. D 95 (2017) 066020 [arXiv:1612.05123] [INSPIRE].
G. Inverso, Generalised Scherk-Schwarz reductions from gauged supergravity, JHEP 12 (2017) 124 [arXiv:1708.02589] [INSPIRE].
E. Malek and H. Samtleben, Ten-dimensional origin of Minkowski vacua in N = 8 supergravity, Phys. Lett. B 776 (2018) 64 [arXiv:1710.02163] [INSPIRE].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistent nonlinear K K reduction of 11 − D supergravity on AdS 7 × S 4 and selfduality in odd dimensions, Phys. Lett. B 469 (1999) 96 [hep-th/9905075] [INSPIRE].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistency of the AdS 7 × S 4 reduction and the origin of selfduality in odd dimensions, Nucl. Phys. B 581 (2000) 179 [hep-th/9911238] [INSPIRE].
B. de Wit and H. Nicolai, The Consistency of the S 7 Truncation in D = 11 Supergravity, Nucl. Phys. B 281 (1987) 211 [INSPIRE].
A. Guarino, D.L. Jafferis and O. Varela, String Theory Origin of Dyonic N = 8 Supergravity and Its Chern-Simons Duals, Phys. Rev. Lett. 115 (2015) 091601 [arXiv:1504.08009] [INSPIRE].
A. Guarino and O. Varela, Consistent \( \mathcal{N}=8 \) truncation of massive IIA on S 6, JHEP 12 (2015) 020 [arXiv:1509.02526] [INSPIRE].
E. Malek, 7-dimensional \( \mathcal{N}=2 \) Consistent Truncations using SL(5) Exceptional Field Theory, JHEP 06 (2017) 026 [arXiv:1612.01692] [INSPIRE].
E. Malek, Half-Maximal Supersymmetry from Exceptional Field Theory, Fortsch. Phys. 65 (2017) 1700061 [arXiv:1707.00714] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supersymmetric Backgrounds and Generalised Special Holonomy, Class. Quant. Grav. 33 (2016) 125026 [arXiv:1411.5721] [INSPIRE].
A. Coimbra and C. Strickland-Constable, Generalised Structures for \( \mathcal{N}=1 \) AdS Backgrounds, JHEP 11 (2016) 092 [arXiv:1504.02465] [INSPIRE].
A. Ashmore, M. Petrini and D. Waldram, The exceptional generalised geometry of supersymmetric AdS flux backgrounds, JHEP 12 (2016) 146 [arXiv:1602.02158] [INSPIRE].
A. Coimbra and C. Strickland-Constable, Supersymmetric Backgrounds, the Killing Superalgebra and Generalised Special Holonomy, JHEP 11 (2016) 063 [arXiv:1606.09304] [INSPIRE].
A. Coimbra and C. Strickland-Constable, Supersymmetric AdS backgrounds and weak generalised holonomy, arXiv:1710.04156 [INSPIRE].
P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum Configurations for Superstrings, Nucl. Phys. B 258 (1985) 46 [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].
F. Apruzzi, M. Fazzi, A. Passias, D. Rosa and A. Tomasiello, AdS 6 solutions of type-II supergravity, JHEP 11 (2014) 099 [Erratum ibid. 1505 (2015) 012] [arXiv:1406.0852] [INSPIRE].
H. Kim, N. Kim and M. Suh, Supersymmetric AdS 6 Solutions of Type IIB Supergravity, Eur. Phys. J. C 75 (2015) 484 [arXiv:1506.05480] [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].
E. D’Hoker, M. Gutperle, A. Karch and C.F. Uhlemann, Warped AdS 6 × S 2 in Type IIB supergravity I: Local solutions, JHEP 08 (2016) 046 [arXiv:1606.01254] [INSPIRE].
E. D’Hoker, M. Gutperle and C.F. Uhlemann, Holographic duals for five-dimensional superconformal quantum field theories, Phys. Rev. Lett. 118 (2017) 101601 [arXiv:1611.09411] [INSPIRE].
E. D’Hoker, M. Gutperle and C.F. Uhlemann, Warped AdS 6 × S 2 in Type IIB supergravity II: Global solutions and five-brane webs, JHEP 05 (2017) 131 [arXiv:1703.08186] [INSPIRE].
E. D’Hoker, M. Gutperle and C.F. Uhlemann, Warped AdS 6 × S 2 in Type IIB supergravity III: Global solutions with seven-branes, JHEP 11 (2017) 200 [arXiv:1706.00433] [INSPIRE].
S. Cremonesi and A. Tomasiello, 6d holographic anomaly match as a continuum limit, JHEP 05 (2016) 031 [arXiv:1512.02225] [INSPIRE].
F. Apruzzi, J.C. Geipel, A. Legramandi, N.T. Macpherson and M. Zagermann, Minkowski 4 × S 2 solutions of IIB supergravity, Fortsch. Phys. 66 (2018) 1800006 [arXiv:1801.00800] [INSPIRE].
P.K. Townsend and P. van Nieuwenhuizen, Gauged seven-dimensional supergravity, Phys. Lett. B 125 (1983) 41 [INSPIRE].
L.J. Romans, The F(4) Gauged Supergravity in Six-dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].
A. Passias, A. Rota and A. Tomasiello, Universal consistent truncation for 6d/7d gauge/gravity duals, JHEP 10 (2015) 187 [arXiv:1506.05462] [INSPIRE].
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].
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].
P. Karndumri and J. Louis, Supersymmetric AdS 6 vacua in six-dimensional N = (1, 1) gauged supergravity, JHEP 01 (2017) 069 [arXiv:1612.00301] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional Field Theory I: E 6(6) covariant Form of M-theory and Type IIB, Phys. Rev. D 89 (2014) 066016 [arXiv:1312.0614] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory. II. E 7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [INSPIRE].
A. Abzalov, I. Bakhmatov and E.T. Musaev, Exceptional field theory: SO(5, 5), JHEP 06 (2015) 088 [arXiv:1504.01523] [INSPIRE].
E.T. Musaev, Exceptional field theory: SL(5), JHEP 02 (2016) 012 [arXiv:1512.02163] [INSPIRE].
B. de Wit and H. Samtleben, Gauged maximal supergravities and hierarchies of nonAbelian vector-tensor systems, Fortsch. Phys. 53 (2005) 442 [hep-th/0501243] [INSPIRE].
J. Louis and S. Lüst, Supersymmetric AdS 7 backgrounds in half-maximal supergravity and marginal operators of (1, 0) SCFTs, JHEP 10 (2015) 120 [arXiv:1506.08040] [INSPIRE].
F. Apruzzi, M. Fazzi, A. Passias and A. Tomasiello, Supersymmetric AdS 5 solutions of massive IIA supergravity, JHEP 06 (2015) 195 [arXiv:1502.06620] [INSPIRE].
A. Ashmore and D. Waldram, Exceptional Calabi-Yau spaces: the geometry of \( \mathcal{N}=2 \) backgrounds with flux, Fortsch. Phys. 65 (2017) 1600109 [arXiv:1510.00022] [INSPIRE].
J. Jeong, Ö. Kelekci and E. Ó Colgáin, An alternative IIB embedding of F(4) gauged supergravity, JHEP 05 (2013) 079 [arXiv:1302.2105] [INSPIRE].
A. Brandhuber and Y. Oz, The D-4-D-8 brane system and five-dimensional fixed points, Phys. Lett. B 460 (1999) 307 [hep-th/9905148] [INSPIRE].
Y. Lozano, N.T. Macpherson and J. Montero, AdS 6 T-duals and type IIB AdS 6 × S 2 geometries with 7-branes, JHEP 01 (2019) 116 [arXiv:1810.08093] [INSPIRE].
O. Bergman, D. Rodríguez-Gómez and C.F. Uhlemann, Testing AdS6/CF T5 in Type IIB with stringy operators, JHEP 08 (2018) 127 [arXiv:1806.07898] [INSPIRE].
M. Fluder and C.F. Uhlemann, Precision Test of AdS 6 /CF T 5 in Type IIB String Theory, Phys. Rev. Lett. 121 (2018) 171603 [arXiv:1806.08374] [INSPIRE].
M. Gutperle, J. Kaidi and H. Raj, Janus solutions in six-dimensional gauged supergravity, JHEP 12 (2017) 018 [arXiv:1709.09204] [INSPIRE].
M. Gutperle, J. Kaidi and H. Raj, Mass deformations of 5d SCFTs via holography, JHEP 02 (2018) 165 [arXiv:1801.00730] [INSPIRE].
S.M. Hosseini, K. Hristov, A. Passias and A. Zaffaroni, 6D attractors and black hole microstates, JHEP 12 (2018) 001 [arXiv:1809.10685] [INSPIRE].
M. Suh, Supersymmetric AdS 6 black holes from matter coupled F (4) gauged supergravity, JHEP 02 (2019) 108 [arXiv:1810.00675] [INSPIRE].
P. Karndumri, Gravity duals of 5D N = 2 SYM theory from F (4) gauged supergravity, Phys. Rev. D 90 (2014) 086009 [arXiv:1403.1150] [INSPIRE].
G.B. De Luca, A. Gnecchi, G. Lo Monaco and A. Tomasiello, Holographic duals of 6d RG flows, JHEP 03 (2019) 035 [arXiv:1810.10013] [INSPIRE].
C.D.A. Blair, E. Malek and J.-H. Park, M-theory and Type IIB from a Duality Manifest Action, JHEP 01 (2014) 172 [arXiv:1311.5109] [INSPIRE].
A. Baguet, O. Hohm and H. Samtleben, E 6(6) Exceptional Field Theory: Review and Embedding of Type IIB, PoS(CORFU2014)133 [arXiv:1506.01065] [INSPIRE].
F. Ciceri, B. de Wit and O. Varela, IIB supergravity and the E 6(6) covariant vector-tensor hierarchy, JHEP 04 (2015) 094 [arXiv:1412.8297] [INSPIRE].
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Malek, E., Samtleben, H. & Camell, V.V. Supersymmetric AdS7 and AdS6 vacua and their consistent truncations with vector multiplets. J. High Energ. Phys. 2019, 88 (2019). https://doi.org/10.1007/JHEP04(2019)088
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DOI: https://doi.org/10.1007/JHEP04(2019)088