Decomposable (4,7) solutions in eleven-dimensional supergravity

ALEKSEEVSKY, Dmitri, Ioannis CHRYSIKOS and Arman TAGHAVI-CHABERT. Decomposable (4,7) solutions in eleven-dimensional supergravity. 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.

Basic information

• Original name: Decomposable (4,7) solutions in eleven-dimensional supergravity
• Authors: ALEKSEEVSKY, Dmitri, Ioannis CHRYSIKOS and Arman TAGHAVI-CHABERT.
• Edition: Classical and Quantum Gravity, Institute of Physics Publishing, 2019, 0264-9381.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: United Kingdom of Great Britain and Northern Ireland
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 3.071
• Doi: http://dx.doi.org/10.1088/1361-6382/ab0615
• UT WoS: 000460058600002
• Keywords in English: supergravity; M-theory; supergravity backgrounds; homogeneous supergravity backgrounds; special geometric structures; G(2)-structures; Einstein metrics
• Tags: RIV ne
• Tags: International impact, Reviewed

Abstract

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.