Supersymmetric domain walls from metrics of special holonomy

Abstract

Supersymmetric domain-wall spacetimes that lift to Ricci-flat solutions of M-theory admit generalized Heisenberg (2-step nilpotent) isometry groups. These metrics may be obtained from known cohomogeneity one metrics of special holonomy by taking a "Heisenberg limit," based on an Inönü-Wigner contraction of the isometry group. Associated with each such metric is an Einstein metric with negative cosmological constant on a solvable group manifold. We discuss the relevance of our metrics to the resolution of singularities in domain-wall spacetimes and some applications to holography. The extremely simple forms of the explicit metrics suggest that they will be useful for many other applications. We also give new but incomplete inhomogeneous metrics of holonomy SU (3), G 2 and Spin(7), which are T 1 , T 2 and T 3 bundles respectively over hyper-Kähler four-manifolds.

Conformally parallel G2 structures on a class of solvmanifolds

“…This last condition is equivalent to (DJ) 2 = (JD) 2 and we show that this is the compatibility that one has to impose between D and the SU(3) structure in order to obtain the non-compact examples found in [17].…”

“…Interesting non-compact examples are provided by Gibbons, Lü, Pope, Stelle in [17], where incomplete Ricci-flat metrics of holonomy G 2 with a 2-step nilpotent isometry group N acting on orbits of codimension one are presented. It turns out that these metrics have scaling symmetries generated by a homothetic Killing vector field, and are locally isometric (modulo a conformal change) to homogeneous metrics on solvable Lie groups.…”

Anti-self-dual metrics on Lie groups

“…The Lie algebra g 0 also features in [7], as one example in a study of Einstein metrics constructed from left-invariant metrics on nilpotent groups. Higher dimensional examples give rise to Einstein metrics on solvable extensions, and related metrics with exceptional holonomy.…”

Conformally parallel Spin(7) structures on solvmanifolds

“…The study of manifolds with exceptional holonomy and the construction of explicit examples is still an active research area in mathematics and related sciences (see also references in [18,25,36,39,38]). …”

“…Other geometries, such as locally conformal hyperkaehler and quaternion Kaehler, were also investigated in the literature [6,8,19,25,30]. Because of the significance of the holonomy group structure in Riemannian geometry, the choices of G 2 and Spin(7) also deserve attention [10,20,22,30,35].…”