Abstract
We discuss the notion of generalised U-duality as a solution generating technique in supergravity. We demonstrate a method to take solutions of type IIA supergravity on a 3-sphere, with NSNS flux, to new solutions of 11-dimensional supergravity, using exceptional geometry techniques. These new solutions are characterised by an underlying 3-algebra structure, and generalise features of solutions obtained by non-abelian T-duality, which involve an underlying ordinary Lie algebra. We focus on an example where we start with the pp-F1-NS5 solution in type IIA supergravity. We discuss the properties of our resulting new solution, including the possibility of viewing it globally as a U-fold, and its M2 and M5 brane charges. In the extremal case, the new solution admits an AdS3 limit, which falls into a recently constructed class of M-theory AdS3 backgrounds — this provides a global completion of our solution with a well-defined holographic dual, similar to the global completions of non-abelian T-dual solutions. Our full solution is a 6-vector deformation of this AdS3 limit. We also explicitly solve the Killing spinor equation in the AdS3 limit, finding a \( \frac{1}{2}\hbox{-} \mathrm{BPS} \) solution.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. C. Thompson, An introduction to generalised dualities and their applications to holography and integrability, PoS CORFU2018 (2019) 099 [arXiv:1904.11561] [INSPIRE].
E. Cremmer and B. Julia, The N = 8 supergravity theory. 1. The Lagrangian, Phys. Lett. B 80 (1978) 48 [INSPIRE].
C. M. Hull and P. K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
X. C. de la Ossa and F. Quevedo, Duality symmetries from non-Abelian isometries in string theory, Nucl. Phys. B 403 (1993) 377 [hep-th/9210021] [INSPIRE].
A. Giveon and M. Roček, On non-Abelian duality, Nucl. Phys. B 421 (1994) 173 [hep-th/9308154] [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 and C. Núñez, Field theory aspects of non-Abelian T-duality and N = 2 linear quivers, JHEP 05 (2016) 107 [arXiv:1603.04440] [INSPIRE].
J. J. Fernandez-Melgarejo, J.-I. Sakamoto, Y. Sakatani and K. Yoshida, T -folds from Yang-Baxter deformations, JHEP 12 (2017) 108 [arXiv:1710.06849] [INSPIRE].
M. Bugden, Non-Abelian T-folds, JHEP 03 (2019) 189 [arXiv:1901.03782] [INSPIRE].
C. Klimčík and P. Ševera, Poisson-Lie T duality and loop groups of Drinfeld doubles, Phys. Lett. B 372 (1996) 65 [hep-th/9512040] [INSPIRE].
C. Klimčík and P. Ševera, Dual non-Abelian duality and the Drinfeld double, Phys. Lett. B 351 (1995) 455 [hep-th/9502122] [INSPIRE].
F. Hassler, Poisson-Lie T-duality in double field theory, Phys. Lett. B 807 (2020) 135455 [arXiv:1707.08624] [INSPIRE].
S. Demulder, F. Hassler and D. C. Thompson, Doubled aspects of generalised dualities and integrable deformations, JHEP 02 (2019) 189 [arXiv:1810.11446] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and D. Waldram, T-duality, generalized geometry and non-geometric backgrounds, JHEP 04 (2009) 075 [arXiv:0807.4527] [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, Fortsch. Phys. 65 (2017) 1700048 [arXiv:1401.3360] [INSPIRE].
G. Itsios, Y. Lozano, E. O Colgain and K. Sfetsos, Non-Abelian T-duality and consistent truncations in type-II supergravity, JHEP 08 (2012) 132 [arXiv:1205.2274] [INSPIRE].
Y. Sakatani, Type II DFT solutions from Poisson-Lie T-duality/plurality, arXiv:1903.12175 [INSPIRE].
A. Catal-Ozer, Non-Abelian T-duality as a transformation in double field theory, JHEP 08 (2019) 115 [arXiv:1904.00362] [INSPIRE].
Y. Sakatani, U -duality extension of Drinfel’d double, PTEP 2020 (2020) 023B08 [arXiv:1911.06320] [INSPIRE].
E. Malek and D. C. Thompson, Poisson-Lie U-duality in exceptional field theory, JHEP 04 (2020) 058 [arXiv:1911.07833] [INSPIRE].
Y. Sakatani and S. Uehara, Non-Abelian U -duality for membranes, PTEP 2020 (2020) 073B01 [arXiv:2001.09983] [INSPIRE].
C. D. A. Blair, D. C. Thompson and S. Zhidkova, Exploring exceptional Drinfel’d geometries, JHEP 09 (2020) 151 [arXiv:2006.12452] [INSPIRE].
E. Malek, Y. Sakatani and D. C. Thompson, E6(6) exceptional Drinfel’d algebras, JHEP 01 (2021) 020 [arXiv:2007.08510] [INSPIRE].
Y. Sakatani, Extended Drinfel’d algebras and non-Abelian duality, PTEP 2021 (2021) 063B02 [arXiv:2009.04454] [INSPIRE].
E. T. Musaev and Y. Sakatani, Non-Abelian U duality at work, Phys. Rev. D 104 (2021) 046015 [arXiv:2012.13263] [INSPIRE].
M. Bugden, O. Hulik, F. Valach and D. Waldram, G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality, Fortsch. Phys. 69 (2021) 2100028 [arXiv:2103.01139] [INSPIRE].
Y. Sakatani, Half-maximal extended Drinfel’d algebras, PTEP 2022 (2022) 013B14 [arXiv:2106.02041] [INSPIRE].
M. Cvetič, H. Lü, C. N. Pope, A. Sadrzadeh and T. A. Tran, S3 and S4 reductions of type IIA supergravity, Nucl. Phys. B 590 (2000) 233 [hep-th/0005137] [INSPIRE].
Y. Lozano, C. Núñez, A. Ramirez and S. Speziali, M -strings and AdS3 solutions to M-theory with small N = (0, 4) supersymmetry, JHEP 08 (2020) 118 [arXiv:2005.06561] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, \( T\overline{T} \) and LST, JHEP 07 (2017) 122 [arXiv:1701.05576] [INSPIRE].
Y. Lozano, N. T. Macpherson, C. Núñez and A. Ramirez, AdS3 solutions in massive IIA with small N = (4, 0) supersymmetry, JHEP 01 (2020) 129 [arXiv:1908.09851] [INSPIRE].
Y. Lozano, N. T. Macpherson, C. Núñez and A. Ramirez, 1/4 BPS solutions and the AdS3/CFT2 correspondence, Phys. Rev. D 101 (2020) 026014 [arXiv:1909.09636] [INSPIRE].
Y. Lozano, N. T. Macpherson, C. Núñez and A. Ramirez, Two dimensional N = (0, 4) quivers dual to AdS3 solutions in massive IIA, JHEP 01 (2020) 140 [arXiv:1909.10510] [INSPIRE].
Y. Lozano, N. T. Macpherson, C. Núñez and A. Ramirez, AdS3 solutions in massive IIA, defect CFTs and T-duality, JHEP 12 (2019) 013 [arXiv:1909.11669] [INSPIRE].
C. Klimčík, η and λ deformations as E-models, Nucl. Phys. B 900 (2015) 259 [arXiv:1508.05832] [INSPIRE].
O. Hohm and H. Samtleben, Consistent Kaluza-Klein truncations via exceptional field theory, JHEP 01 (2015) 131 [arXiv:1410.8145] [INSPIRE].
D. S. Berman and C. D. A. Blair, The geometry, branes and applications of exceptional field theory, Int. J. Mod. Phys. A 35 (2020) 2030014 [arXiv:2006.09777] [INSPIRE].
C. D. A. Blair and E. Malek, Geometry and fluxes of SL(5) exceptional field theory, JHEP 03 (2015) 144 [arXiv:1412.0635] [INSPIRE].
R. Terrisse, D. Tsimpis and C. A. Whiting, D-branes and non-Abelian T-duality, Nucl. Phys. B 947 (2019) 114733 [arXiv:1811.05800] [INSPIRE].
D. S. Berman, H. Godazgar, M. J. Perry and P. West, Duality invariant actions and generalised geometry, JHEP 02 (2012) 108 [arXiv:1111.0459] [INSPIRE].
K. Lee, S.-J. Rey and Y. Sakatani, Effective action for non-geometric fluxes duality covariant actions, JHEP 07 (2017) 075 [arXiv:1612.08738] [INSPIRE].
J. Aguilera-Damia, L. M. Anderson and E. Coleman, A substrate for brane shells from \( T\overline{T} \), JHEP 05 (2021) 248 [arXiv:2012.09802] [INSPIRE].
O. Aharony, M. Berkooz, D. Kutasov and N. Seiberg, Linear dilatons, NS five-branes and holography, JHEP 10 (1998) 004 [hep-th/9808149] [INSPIRE].
A. Giveon, D. Kutasov and O. Pelc, Holography for noncritical superstrings, JHEP 10 (1999) 035 [hep-th/9907178] [INSPIRE].
T. Ortin, Gravity and strings, Cambridge University Press, Cambridge, U.K. (2004).
H. Lü, C. N. Pope and J. Rahmfeld, A construction of Killing spinors on Sn , J. Math. Phys. 40 (1999) 4518 [hep-th/9805151] [INSPIRE].
S. Zacarias, Marginal deformations of a class of AdS3 N = (0, 4) holographic backgrounds, JHEP 06 (2021) 017 [arXiv:2102.05681] [INSPIRE].
G. Inverso, Generalised Scherk-Schwarz reductions from gauged supergravity, JHEP 12 (2017) 124 [Erratum ibid. 06 (2021) 148] [arXiv:1708.02589] [INSPIRE].
O. Kelekci, Y. Lozano, N. T. Macpherson and E. O. Colgáin, Supersymmetry and non-Abelian T-duality in type-II supergravity, Class. Quant. Grav. 32 (2015) 035014 [arXiv:1409.7406] [INSPIRE].
P. Karndumri and P. Nuchino, Supersymmetric domain walls in 7D maximal gauged supergravity, Eur. Phys. J. C 79 (2019) 648 [arXiv:1904.02871] [INSPIRE].
P. Karndumri and P. Nuchino, Supersymmetric solutions of 7D maximal gauged supergravity, Phys. Rev. D 101 (2020) 086012 [arXiv:1910.02909] [INSPIRE].
P. Karndumri and P. Nuchino, Twisted compactifications of 6D field theories from maximal 7D gauged supergravity, Eur. Phys. J. C 80 (2020) 201 [arXiv:1912.04807] [INSPIRE].
S. Chakraborty, A. Giveon and D. Kutasov, \( T\overline{T} \), \( J\overline{T} \), \( T\overline{J} \) and string theory, J. Phys. A 52 (2019) 384003 [arXiv:1905.00051] [INSPIRE].
L. Apolo, S. Detournay and W. Song, TsT, \( T\overline{T} \) and black strings, JHEP 06 (2020) 109 [arXiv:1911.12359] [INSPIRE].
K. Gubarev and E. T. Musaev, Polyvector deformations in eleven-dimensional supergravity, Phys. Rev. D 103 (2021) 066021 [arXiv:2011.11424] [INSPIRE].
S. Chakraborty, A. Giveon and D. Kutasov, \( T\overline{T} \), black holes and negative strings, JHEP 09 (2020) 057 [arXiv:2006.13249] [INSPIRE].
M. Cvetič, H. Lü and C. N. Pope, Consistent Kaluza-Klein sphere reductions, Phys. Rev. D 62 (2000) 064028 [hep-th/0003286] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2203.01838
Rights and permissions
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.
About this article
Cite this article
Blair, C.D.A., Zhidkova, S. Generalised U-dual solutions in supergravity. J. High Energ. Phys. 2022, 81 (2022). https://doi.org/10.1007/JHEP05(2022)081
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2022)081