Decomposable (4,7) solutions in eleven-dimensional supergravity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50015541" target="_blank" >RIV/62690094:18470/19:50015541 - isvavai.cz</a>
Result on the web
<a href="https://iopscience.iop.org/article/10.1088/1361-6382/ab0615/meta" target="_blank" >https://iopscience.iop.org/article/10.1088/1361-6382/ab0615/meta</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1361-6382/ab0615" target="_blank" >10.1088/1361-6382/ab0615</a>
Alternative languages
Result language
angličtina
Original language name
Decomposable (4,7) solutions in eleven-dimensional supergravity
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-00496S" target="_blank" >GA18-00496S: Singular spaces from special holonomy and foliations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Classical and quantum gravity
ISSN
0264-9381
e-ISSN
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Volume of the periodical
36
Issue of the periodical within the volume
7
Country of publishing house
GB - UNITED KINGDOM
Number of pages
27
Pages from-to
1-27
UT code for WoS article
000460058600002
EID of the result in the Scopus database
2-s2.0-85064089104