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ALEKSEEVSKY, Dmitri, Ioannis CHRYSIKOS a Arman TAGHAVI-CHABERT. Decomposable (4,7) solutions in eleven-dimensional supergravity. Classical and Quantum Gravity. Institute of Physics Publishing, 2019, roč. 36, č. 7, s. 1-28. ISSN 0264-9381. Dostupné z: https://dx.doi.org/10.1088/1361-6382/ab0615.

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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  -

Základní údaje
Originální název	Decomposable (4,7) solutions in eleven-dimensional supergravity
Autoři	ALEKSEEVSKY, Dmitri, Ioannis CHRYSIKOS a Arman TAGHAVI-CHABERT.
Vydání	Classical and Quantum Gravity, Institute of Physics Publishing, 2019, 0264-9381.

Další údaje
Originální jazyk	angličtina
Typ výsledku	Článek v odborném periodiku
Obor	10101 Pure mathematics
Stát vydavatele	Velká Británie a Severní Irsko
Utajení	není předmětem státního či obchodního tajemství
WWW	URL
Impakt faktor	Impact factor: 3.071
Doi	http://dx.doi.org/10.1088/1361-6382/ab0615
UT WoS	000460058600002
Klíčová slova anglicky	supergravity; M-theory; supergravity backgrounds; homogeneous supergravity backgrounds; special geometric structures; G(2)-structures; Einstein metrics
Štítky	RIV ne
Příznaky	Mezinárodní význam, Recenzováno
Změnil	Změnila: Mgr. Marie Šípková, DiS., učo 437722. Změněno: 26. 5. 2023 11:45.

Anotace
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.

Anotace

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.