Decomposable $(5,6)$-solutions in eleven-dimensional supergravity

TL;DR

This paper constructs new decomposable (5,6)-solutions in eleven-dimensional supergravity, exploring various flux forms and geometric structures, including Ricci-isotropic Walker manifolds and Einstein-Kähler manifolds, expanding known classes of solutions.

Contribution

It introduces novel decomposable (5,6)-supergravity backgrounds using diverse flux forms and geometric configurations, extending previous classifications and including infinitely many non-symmetric solutions.

Findings

Constructed solutions with null flux forms on Ricci-isotropic Walker manifolds.

Extended known solutions to include products of Einstein and Kähler-Einstein manifolds.

Produced infinitely many non-symmetric backgrounds using Einstein-Sasakian structures.

Abstract

We present decomposable (5,6)-solutions $\widetilde{M}^{1,4} \times M^6$ in eleven-dimensional supergravity by solving the bosonic supergravity equations for a variety of non-trivial flux forms. Many of the bosonic backgrounds presented here are induced by various types of null flux forms on products of certain totally Ricci-isotropic Lorentzian Walker manifolds and Ricci-flat Riemannian manifolds. These constructions provide an analogue of work done by I. Chrysikos and A. Galaev who made similar computations 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 K\"ahler-Einstein manifolds with positive Einstein constant. This conclusion generalizes a result of C. N. Pope and P. van Nieuwenhuizen concerning the appearance of six-dimensional K\"ahler-Einstein manifolds in eleven-dimensional supergravity. In this setting we construct infinitely many non-symmetric decomposable (5, 6)-supergravity backgrounds by using the infinitely many Lorentzian Einstein-Sasakian structures with negative Einstein constant on the 5-sphere, known from the work of C. P. Boyer et al.