Decomposable $(5,6)$solutions in elevendimensional supergravity
Abstract
We present decomposable (5,6)solutions $\widetilde{M}^{1,4} \times M^6$ in elevendimensional supergravity by solving the bosonic supergravity equations for a variety of nontrivial flux forms. Many of the bosonic backgrounds presented here are induced by various types of null flux forms on products of certain totally Ricciisotropic Lorentzian Walker manifolds and Ricciflat Riemannian manifolds. These constructions provide an analogue of the work in [CG20], where similar computations were made for decomposable (6,5)solutions. We also present bosonic backgrounds that are products of Lorentzian Einstein manifolds with negative Einstein constant (in the "mostly plus" convention) and Riemannian KählerEinstein manifolds with positive Einstein constant. This conclusion generalizes a result of C. N. Pope et al. [PN89] concerning the appearance of sixdimensional KählerEinstein manifolds in elevendimensional supergravity. In this setting, we construct infinitely many nonsymmetric decomposable (5, 6)supergravity backgrounds, by using the infinitely many Lorentzian EinsteinSasakian structures with negative Einstein constant on the 5sphere, known from the work of C. P. Boyer et al. [BGM06].
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.10084
 Bibcode:
 2021arXiv211010084C
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 83E50
 EPrint:
 30 pages