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@article{2285881, author = {Alekseevsky, Dmitri and Chrysikos, Ioannis and TaghaviandChabert, Arman}, article_number = {7}, doi = {http://dx.doi.org/10.1088/1361-6382/ab0615}, keywords = {supergravity; M-theory; supergravity backgrounds; homogeneous supergravity backgrounds; special geometric structures; G(2)-structures; Einstein metrics}, language = {eng}, issn = {0264-9381}, journal = {Classical and Quantum Gravity}, note = {Nevykazovat do RIV. Afiliace není navázána na MU.}, title = {Decomposable (4,7) solutions in eleven-dimensional supergravity}, url = {https://iopscience.iop.org/article/10.1088/1361-6382/ab0615}, volume = {36}, year = {2019} }
TY - JOUR ID - 2285881 AU - Alekseevsky, Dmitri - Chrysikos, Ioannis - Taghavi-Chabert, Arman PY - 2019 TI - Decomposable (4,7) solutions in eleven-dimensional supergravity JF - Classical and Quantum Gravity VL - 36 IS - 7 SP - 1-28 EP - 1-28 PB - Institute of Physics Publishing SN - 02649381 N1 - Nevykazovat do RIV. Afiliace není navázána na MU. KW - supergravity KW - M-theory KW - supergravity backgrounds KW - homogeneous supergravity backgrounds KW - special geometric structures KW - G(2)-structures KW - Einstein metrics UR - https://iopscience.iop.org/article/10.1088/1361-6382/ab0615 N2 - We describe a class of decomposable eleven-dimensional supergravity backgrounds (M-10,M-1 = (M) over tilde (3,1) x M-7, gM = (g) over tilde + g) which arc products of a four-dimensional Lorentzian manifold and a seven-dimensional Riemannian manifold, endowed with a flux form given in terms of the volume form on (M) over tilde (3,1) and a closed 4-form F-4 on M-7. We show that the Maxwell equation for such a flux form can be read in terms of the co-closed 3-form phi = *F-7(4). Moreover, the supergravity equation reduces to the condition that ((M) over tilde (3,1),(g) over tilde) is an Einstein manifold with negative Einstein constant and (M-7,g,F) is a Riemannian manifold which satisfies the Einstein equation with a stress-energy tensor associated to the 3-form phi. Whenever this 3-form is generic, we show that the Maxwell equation induces a weak G2-structure on M-7 and obtain decomposable supergravity backgrounds given by the product of a weak G(2) -manifold (M-7,phi,g) with a Lorentzian Einstein manifold ((M) over tilde (3,1),(g) over tilde). We also construct examples of compact homogeneous Riemannian 7-manifolds endowed with non-generic invariant 3-forms which satisfy the Maxwell equation, but the construction of decomposable homogeneous supergravity backgrounds of this type remains an open problem. ER -
ALEKSEEVSKY, Dmitri, Ioannis CHRYSIKOS and Arman TAGHAVI-CHABERT. Decomposable (4,7) solutions in eleven-dimensional supergravity. \textit{Classical and Quantum Gravity}. Institute of Physics Publishing, 2019, vol.~36, No~7, p.~1-28. ISSN~0264-9381. Available from: https://dx.doi.org/10.1088/1361-6382/ab0615.
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