Publication details
Decomposable (4,7) solutions in eleven-dimensional supergravity
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Classical and Quantum Gravity |
| Citation | |
| Web | https://iopscience.iop.org/article/10.1088/1361-6382/ab0615 |
| 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 |
| 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. |