Abstract
In this paper, we construct non-trivial solutions to the 2D-dimensional field equations of Double Field Theory (DFT) by using a consistent Scherk-Schwarz ansatz. The ansatz identifies 2(D − d) internal directions with a twist U M N which is directly connected to the covariant fluxes \( \mathcal{F} \) ABC . It exhibits 2(D − d) linear independent generalized Killing vectors K I J and gives rise to a gauged supergravity in d dimensions. We analyze the covariant fluxes and the corresponding gauged supergravity with a Minkowski vacuum. We calculate fluctuations around such vacua and show how they gives rise to massive scalars field and vectors field with a non-abelian gauge algebra. Because DFT is a background independent theory, these fields should directly correspond the string excitations in the corresponding background. For (D − d) = 3 we perform a complete scan of all allowed covariant fluxes and find two different kinds of backgrounds: the single and the double elliptic case. The later is not T-dual to a geometric background and cannot be transformed to a geometric setting by a field redefinition either. While this background fulfills the strong constraint, it is still consistent with the Killing vectors depending on the coordinates and the winding coordinates, thereby giving a non-geometric patching. This background can therefore not be described in Supergravity or Generalized Geometry.
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References
A. Dabholkar and C. Hull, Generalised T-duality and non-geometric backgrounds, JHEP 05 (2006) 009 [hep-th/0512005] [INSPIRE].
R. Blumenhagen and E. Plauschinn, Nonassociative Gravity in String Theory?, J. Phys. A 44 (2011) 015401 [arXiv:1010.1263] [INSPIRE].
D. Lüst, T-duality and closed string non-commutative (doubled) geometry, JHEP 12 (2010) 084 [arXiv:1010.1361] [INSPIRE].
R. Blumenhagen, A. Deser, D. Lüst, E. Plauschinn and F. Rennecke, Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry, J. Phys. A 44 (2011) 385401 [arXiv:1106.0316] [INSPIRE].
C. Condeescu, I. Florakis and D. Lüst, Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory, JHEP 04 (2012) 121 [arXiv:1202.6366] [INSPIRE].
D. Andriot, M. Larfors, D. Lüst and P. Patalong, (Non-)commutative closed string on T-dual toroidal backgrounds, JHEP 06 (2013) 021 [arXiv:1211.6437] [INSPIRE].
D. Mylonas, P. Schupp and R.J. Szabo, Membrane σ-models and Quantization of Non-Geometric Flux Backgrounds, JHEP 09 (2012) 012 [arXiv:1207.0926] [INSPIRE].
I. Bakas and D. Lüst, 3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua, JHEP 01 (2014) 171 [arXiv:1309.3172] [INSPIRE].
R. Blumenhagen, M. Fuchs, F. Hassler, D. Lüst and R. Sun, Non-associative Deformations of Geometry in Double Field Theory, arXiv:1312.0719 [INSPIRE].
D. Mylonas, P. Schupp and R.J. Szabo, Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics, arXiv:1312.1621 [INSPIRE].
D. Andriot, M. Larfors, D. Lüst and P. Patalong, A ten-dimensional action for non-geometric fluxes, JHEP 09 (2011) 134 [arXiv:1106.4015] [INSPIRE].
D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, A geometric action for non-geometric fluxes, Phys. Rev. Lett. 108 (2012) 261602 [arXiv:1202.3060] [INSPIRE].
D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, Non-Geometric Fluxes in Supergravity and Double Field Theory, Fortsch. Phys. 60 (2012) 1150 [arXiv:1204.1979] [INSPIRE].
R. Blumenhagen, A. Deser, E. Plauschinn and F. Rennecke, A bi-invariant Einstein-Hilbert action for the non-geometric string, Phys. Lett. B 720 (2013) 215 [arXiv:1210.1591] [INSPIRE].
R. Blumenhagen, A. Deser, E. Plauschinn and F. Rennecke, Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids, JHEP 02 (2013) 122 [arXiv:1211.0030] [INSPIRE].
R. Blumenhagen, A. Deser, E. Plauschinn, F. Rennecke and C. Schmid, The Intriguing Structure of Non-geometric Frames in String Theory, Fortsch. Phys. 61 (2013) 893 [arXiv:1304.2784] [INSPIRE].
D. Andriot and A. Betz, β-supergravity: a ten-dimensional theory with non-geometric fluxes and its geometric framework, JHEP 12 (2013) 083 [arXiv:1306.4381] [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].
C. Hull and B. Zwiebach, The Gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].
J. Scherk and J.H. Schwarz, Spontaneous Breaking of Supersymmetry Through Dimensional Reduction, Phys. Lett. B 82 (1979) 60 [INSPIRE].
J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys. B 153 (1979) 61 [INSPIRE].
G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of Double Field Theory, JHEP 11 (2011) 052 [Erratum ibid. 1111 (2011) 109] [arXiv:1109.0290] [INSPIRE].
M. Graña and D. Marques, Gauged Double Field Theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, arXiv:1401.3360 [INSPIRE].
H. Samtleben, Lectures on Gauged Supergravity and Flux Compactifications, Class. Quant. Grav. 25 (2008) 214002 [arXiv:0808.4076] [INSPIRE].
O. Hohm and S.K. Kwak, Massive Type II in Double Field Theory, JHEP 11 (2011) 086 [arXiv:1108.4937] [INSPIRE].
J.M. Pons and P. Talavera, Consistent and inconsistent truncations: Some results and the issue of the correct uplifting of solutions: old-title = Consistent and inconsistent truncations: General results and the issue of the correct uplifting of solutions, Nucl. Phys. B 678 (2004) 427 [hep-th/0309079] [INSPIRE].
D. Geissbuhler, D. Marques, C. Núñez and V. Penas, Exploring Double Field Theory, JHEP 06 (2013) 101 [arXiv:1304.1472] [INSPIRE].
R. Blumenhagen, X. Gao, D. Herschmann and P. Shukla, Dimensional Oxidation of Non-geometric Fluxes in Type II Orientifolds, arXiv:1306.2761 [INSPIRE].
O. Hohm, D. Lüst and B. Zwiebach, The Spacetime of Double Field Theory: Review, Remarks and Outlook, Fortsch. Phys. 61 (2013) 926 [arXiv:1309.2977] [INSPIRE].
L. Susskind, The Anthropic landscape of string theory, hep-th/0302219 [INSPIRE].
S. Ashok and M.R. Douglas, Counting flux vacua, JHEP 01 (2004) 060 [hep-th/0307049] [INSPIRE].
C. Condeescu, I. Florakis, C. Kounnas and D. Lüst, Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT‘s, JHEP 10 (2013) 057 [arXiv:1307.0999] [INSPIRE].
O. Hohm and S.K. Kwak, Frame-like Geometry of Double Field Theory, J. Phys. A 44 (2011) 085404 [arXiv:1011.4101] [INSPIRE].
D. Geissbuhler, Double Field Theory and N = 4 Gauged Supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].
O. Hohm and B. Zwiebach, On the Riemann Tensor in Double Field Theory, JHEP 05 (2012) 126 [arXiv:1112.5296] [INSPIRE].
I.T. Ellwood, NS-NS fluxes in Hitchin’s generalized geometry, JHEP 12 (2007) 084 [hep-th/0612100] [INSPIRE].
G. Aldazabal, D. Marques and C. Núñez, Double Field Theory: A Pedagogical Review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].
J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].
F. Hassler and D. Lüst, Non-commutative/non-associative IIA ( IIB) Q- and R-branes and their intersections, JHEP 07 (2013) 048 [arXiv:1303.1413] [INSPIRE].
O. Hohm and H. Samtleben, Gauge theory of Kaluza-Klein and winding modes, Phys. Rev. D 88 (2013) 085005 [arXiv:1307.0039] [INSPIRE].
N. Kaloper and R.C. Myers, The Odd story of massive supergravity, JHEP 05 (1999) 010 [hep-th/9901045] [INSPIRE].
O. Hohm and S.K. Kwak, Double Field Theory Formulation of Heterotic Strings, JHEP 06 (2011) 096 [arXiv:1103.2136] [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].
A. Dabholkar and C. Hull, Duality twists, orbifolds and fluxes, JHEP 09 (2003) 054 [hep-th/0210209] [INSPIRE].
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Hassler, F., Lüst, D. Consistent compactification of double field theory on non-geometric flux backgrounds. J. High Energ. Phys. 2014, 85 (2014). https://doi.org/10.1007/JHEP05(2014)085
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DOI: https://doi.org/10.1007/JHEP05(2014)085