Abstract
An extended field theory is presented that captures the full SL(2) × O(6, 6 + n) duality group of four-dimensional half-maximal supergravities. The theory has section constraints whose two inequivalent solutions correspond to minimal D = 10 supergravity and chiral half-maximal D = 6 supergravity, respectively coupled to vector and tensor multiplets. The relation with O(6, 6 + n) (heterotic) double field theory is thoroughly discussed. Non-Abelian interactions as well as background fluxes are captured by a deformation of the generalised diffeomorphisms. Finally, making use of the SL(2) duality structure, it is shown how to generate gaugings with non-trivial de Roo-Wagemans angles via generalised Scherk-Schwarz ansätze. Such gaugings allow for moduli stabilisation including the SL(2) dilaton.
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A. Coimbra, C. Strickland-Constable and D. Waldram, \( {E}_{d(d)}\times {\mathrm{\mathbb{R}}}^{+} \) 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: \( {E}_{d(d)}\times {\mathrm{\mathbb{R}}}^{+} \) and M-theory, JHEP 03 (2014) 019 [arXiv:1212.1586] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional Form of D = 11 Supergravity, Phys. Rev. Lett. 111 (2013) 231601 [arXiv:1308.1673] [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].
O. Hohm and H. Samtleben, Exceptional field theory. III. E 8(8), Phys. Rev. D 90 (2014) 066002 [arXiv:1406.3348] [INSPIRE].
W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [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].
E.T. Musaev, Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions, JHEP 05 (2013) 161 [arXiv:1301.0467] [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, 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].
C. Strickland-Constable, Subsectors, Dynkin Diagrams and New Generalised Geometries, arXiv:1310.4196 [INSPIRE].
E. Malek, From Exceptional Field Theory to Heterotic Double Field Theory via K3, JHEP 03 (2017) 057 [arXiv:1612.01990] [INSPIRE].
A.H. Chamseddine, N=4 Supergravity Coupled to N = 4 Matter, Nucl. Phys. B 185 (1981) 403 [INSPIRE].
E. Bergshoeff, M. de Roo, B. de Wit and P. van Nieuwenhuizen, Ten-Dimensional Maxwell-Einstein Supergravity, Its Currents and the Issue of Its Auxiliary Fields, Nucl. Phys. B 195 (1982) 97 [INSPIRE].
P.K. Townsend, A New Anomaly Free Chiral Supergravity Theory From Compactification on K3, Phys. Lett. B 139 (1984) 283 [INSPIRE].
M. Awada, P.K. Townsend and G. Sierra, Six-dimensional Simple and Extended Chiral Supergravity in Superspace, Class. Quant. Grav. 2 (1985) L85 [INSPIRE].
L.J. Romans, Selfduality for Interacting Fields: Covariant Field Equations for Six-dimensional Chiral Supergravities, Nucl. Phys. B 276 (1986) 71 [INSPIRE].
I. Schnakenburg and P.C. West, Kac-Moody symmetries of ten-dimensional nonmaximal supergravity theories, JHEP 05 (2004) 019 [hep-th/0401196] [INSPIRE].
E.A. Bergshoeff, J. Gomis, T.A. Nutma and D. Roest, Kac-Moody Spectrum of (Half-)Maximal Supergravities, JHEP 02 (2008) 069 [arXiv:0711.2035] [INSPIRE].
P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [INSPIRE].
N. Hitchin, Brackets, forms and invariant functionals, math/0508618 [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].
D. Geissbuhler, Double Field Theory and N = 4 Gauged Supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].
M. Graña and D. Marques, Gauged Double Field Theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].
M. de Roo and P. Wagemans, Gauge Matter Coupling in N = 4 Supergravity, Nucl. Phys. B 262 (1985) 644 [INSPIRE].
J. Schon and M. Weidner, Gauged N = 4 supergravities, JHEP 05 (2006) 034 [hep-th/0602024] [INSPIRE].
M. de Roo, D.B. Westra and S. Panda, de Sitter solutions in N = 4 matter coupled supergravity, JHEP 02 (2003) 003 [hep-th/0212216] [INSPIRE].
M. de Roo, D.B. Westra, S. Panda and M. Trigiante, Potential and mass matrix in gauged N =4 supergravity, JHEP 11 (2003) 022 [hep-th/0310187] [INSPIRE].
G. Dibitetto, A. Guarino and D. Roest, How to halve maximal supergravity, JHEP 06 (2011) 030 [arXiv:1104.3587] [INSPIRE].
C.M. Hull, Noncompact Gaugings of N = 8 Supergravity, Phys. Lett. B 142 (1984) 39 [INSPIRE].
C.M. Hull, More Gaugings of N = 8 Supergravity, Phys. Lett. B 148 (1984) 297 [INSPIRE].
G. Dall’Agata and G. Inverso, On the Vacua of N = 8 Gauged Supergravity in 4 Dimensions, Nucl. Phys. B 859 (2012) 70 [arXiv:1112.3345] [INSPIRE].
G. Dibitetto, A. Guarino and D. Roest, Exceptional Flux Compactifications, JHEP 05 (2012) 056 [arXiv:1202.0770] [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].
A. Guarino, CSO c superpotentials, Nucl. Phys. B 900 (2015) 501 [arXiv:1508.05055] [INSPIRE].
G. Dall’Agata, G. Inverso and M. Trigiante, Evidence for a family of SO(8) gauged supergravity theories, Phys. Rev. Lett. 109 (2012) 201301 [arXiv:1209.0760] [INSPIRE].
G. Dall’Agata, G. Inverso and A. Marrani, Symplectic Deformations of Gauged Maximal Supergravity, JHEP 07 (2014) 133 [arXiv:1405.2437] [INSPIRE].
A. Guarino and O. Varela, Dyonic ISO(7) supergravity and the duality hierarchy, JHEP 02 (2016) 079 [arXiv:1508.04432] [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].
M.P. Hertzberg, S. Kachru, W. Taylor and M. Tegmark, Inflationary Constraints on Type IIA String Theory, JHEP 12 (2007) 095 [arXiv:0711.2512] [INSPIRE].
S. Hellerman, J. McGreevy and B. Williams, Geometric constructions of nongeometric string theories, JHEP 01 (2004) 024 [hep-th/0208174] [INSPIRE].
A. Dabholkar and C. Hull, Duality twists, orbifolds and fluxes, JHEP 09 (2003) 054 [hep-th/0210209] [INSPIRE].
S. Kachru, M.B. Schulz, P.K. Tripathy and S.P. Trivedi, New supersymmetric string compactifications, JHEP 03 (2003) 061 [hep-th/0211182] [INSPIRE].
J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].
G. Aldazabal, P.G. Camara, A. Font and L.E. Ibáñez, More dual fluxes and moduli fixing, JHEP 05 (2006) 070 [hep-th/0602089] [INSPIRE].
G. Dibitetto, J.J. Fernández-Melgarejo and D. Marqués, All gaugings and stable de Sitter in D = 7 half-maximal supergravity, JHEP 11 (2015) 037 [arXiv:1506.01294] [INSPIRE].
B. de Carlos, A. Guarino and J.M. Moreno, Flux moduli stabilisation, Supergravity algebras and no-go theorems, JHEP 01 (2010) 012 [arXiv:0907.5580] [INSPIRE].
B. de Carlos, A. Guarino and J.M. Moreno, Complete classification of Minkowski vacua in generalised flux models, JHEP 02 (2010) 076 [arXiv:0911.2876] [INSPIRE].
U. Danielsson and G. Dibitetto, On the distribution of stable de Sitter vacua, JHEP 03 (2013) 018 [arXiv:1212.4984] [INSPIRE].
N. Kaloper and R.C. Myers, The Odd story of massive supergravity, JHEP 05 (1999) 010 [hep-th/9901045] [INSPIRE].
M. de Roo, M.G.C. Eenink, D.B. Westra and S. Panda, Group manifold reduction of dual N = 1 D = 10 supergravity, JHEP 06 (2005) 077 [hep-th/0503059] [INSPIRE].
D. Roest, Gaugings at angles from orientifold reductions, Class. Quant. Grav. 26 (2009) 135009 [arXiv:0902.0479] [INSPIRE].
G. Dall’Agata, G. Villadoro and F. Zwirner, Type- IIA flux compactifications and N = 4 gauged supergravities, JHEP 08 (2009) 018 [arXiv:0906.0370] [INSPIRE].
G. Dibitetto, R. Linares and D. Roest, Flux Compactifications, Gauge Algebras and de Sitter, Phys. Lett. B 688 (2010) 96 [arXiv:1001.3982] [INSPIRE].
G. Dibitetto, A. Guarino and D. Roest, Charting the landscape of N = 4 flux compactifications, JHEP 03 (2011) 137 [arXiv:1102.0239] [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, New gaugings and non-geometry, arXiv:1506.03457 [INSPIRE].
G. Dibitetto, J.J. Fernandez-Melgarejo, D. Marques and D. Roest, Duality orbits of non-geometric fluxes, Fortsch. Phys. 60 (2012) 1123 [arXiv:1203.6562] [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].
B. de Wit, H. Nicolai and H. Samtleben, Gauged Supergravities, Tensor Hierarchies and M-theory, JHEP 02 (2008) 044 [arXiv:0801.1294] [INSPIRE].
B. de Wit and H. Samtleben, The End of the p-form hierarchy, JHEP 08 (2008) 015 [arXiv:0805.4767] [INSPIRE].
O. Hohm and H. Samtleben, Gauge theory of Kaluza-Klein and winding modes, Phys. Rev. D 88 (2013) 085005 [arXiv:1307.0039] [INSPIRE].
O. Hohm and S.K. Kwak, Double Field Theory Formulation of Heterotic Strings, JHEP 06 (2011) 096 [arXiv:1103.2136] [INSPIRE].
F. Ciceri, A. Guarino and G. Inverso, The exceptional story of massive IIA supergravity, JHEP 08 (2016) 154 [arXiv:1604.08602] [INSPIRE].
G. Inverso, Electric-magnetic deformations of D = 4 gauged supergravities, JHEP 03 (2016) 138 [arXiv:1512.04500] [INSPIRE].
F. Giani, M. Pernici and P. van Nieuwenhuizen, Gauged N = 4 D = 6 supergravity, Phys. Rev. D 30 (1984) 1680 [INSPIRE].
L.J. Romans, The F(4) Gauged Supergravity in Six-dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].
G. Dibitetto, A. Guarino and D. Roest, Lobotomy of Flux Compactifications, JHEP 05 (2014) 067 [arXiv:1402.4478] [INSPIRE].
O. Hohm, S.K. Kwak and B. Zwiebach, Double Field Theory of Type II Strings, JHEP 09 (2011) 013 [arXiv:1107.0008] [INSPIRE].
J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys. B 153 (1979) 61 [INSPIRE].
B. de Wit, H. Samtleben and M. Trigiante, Magnetic charges in local field theory, JHEP 09 (2005) 016 [hep-th/0507289] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [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].
E. Malek, 7-dimensional \( \mathcal{N}=2 \) Consistent Truncations using SL(5) Exceptional Field Theory, arXiv:1612.01692 [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].
D. Geissbuhler, D. Marques, C. Núñez and V. Penas, Exploring Double Field Theory, JHEP 06 (2013) 101 [arXiv:1304.1472] [INSPIRE].
G. Aldazabal, M. Graña, D. Marqués and J.A. Rosabal, Extended geometry and gauged maximal supergravity, JHEP 06 (2013) 046 [arXiv:1302.5419] [INSPIRE].
M. Cederwall, J. Edlund and A. Karlsson, Exceptional geometry and tensor fields, JHEP 07 (2013) 028 [arXiv:1302.6736] [INSPIRE].
C.M. Hull, A Geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
C.M. Hull, Doubled Geometry and T-Folds, JHEP 07 (2007) 080 [hep-th/0605149] [INSPIRE].
G. Dall’Agata, G. Inverso and M. Trigiante, Evidence for a family of SO(8) gauged supergravity theories, Phys. Rev. Lett. 109 (2012) 201301 [arXiv:1209.0760] [INSPIRE].
B. de Wit and H. Nicolai, N=8 Supergravity, Nucl. Phys. B 208 (1982) 323 [INSPIRE].
B. de Wit and H. Nicolai, Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions, JHEP 05 (2013) 077 [arXiv:1302.6219] [INSPIRE].
W. Cho, J.J. Fernández-Melgarejo, I. Jeon and J.-H. Park, Supersymmetric gauged double field theory: systematic derivation by virtue of twist, JHEP 08 (2015) 084 [arXiv:1505.01301] [INSPIRE].
G. Aldazabal, M. Graña, D. Marqués and J.A. Rosabal, The gauge structure of Exceptional Field Theories and the tensor hierarchy, JHEP 04 (2014) 049 [arXiv:1312.4549] [INSPIRE].
G. Aldazabal, D. Marques, C. Núñez and J.A. Rosabal, On Type IIB moduli stabilization and N = 4,8 supergravities, Nucl. Phys. B 849 (2011) 80 [arXiv:1101.5954] [INSPIRE].
D. Andriot and A. Betz, NS-branes, source corrected Bianchi identities and more on backgrounds with non-geometric fluxes, JHEP 07 (2014) 059 [arXiv:1402.5972] [INSPIRE].
S. Gurrieri, A. Lukas and A. Micu, Heterotic on half-flat, Phys. Rev. D 70 (2004) 126009 [hep-th/0408121] [INSPIRE].
J.-P. Derendinger, C. Kounnas, P.M. Petropoulos and F. Zwirner, Superpotentials in IIA compactifications with general fluxes, Nucl. Phys. B 715 (2005) 211 [hep-th/0411276] [INSPIRE].
B. de Carlos, S. Gurrieri, A. Lukas and A. Micu, Moduli stabilisation in heterotic string compactifications, JHEP 03 (2006) 005 [hep-th/0507173] [INSPIRE].
A. Le Diffon and H. Samtleben, Supergravities without an Action: Gauging the Trombone, Nucl. Phys. B 811 (2009) 1 [arXiv:0809.5180] [INSPIRE].
A. Le Diffon, H. Samtleben and M. Trigiante, N=8 Supergravity with Local Scaling Symmetry, JHEP 04 (2011) 079 [arXiv:1103.2785] [INSPIRE].
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Ciceri, F., Dibitetto, G., Fernandez-Melgarejo, J.J. et al. Double field theory at SL(2) angles. J. High Energ. Phys. 2017, 28 (2017). https://doi.org/10.1007/JHEP05(2017)028
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DOI: https://doi.org/10.1007/JHEP05(2017)028