Four-Dimensional N=2(4) Superstring Backgrounds and The Real Heavens

We study N=2(4) superstring backgrounds which are four-dimensional non-\Kahlerian with non-trivial dilaton and torsion fields. In particular we consider the case that the backgrounds possess at least one $U(1)$ isometry and are characterized by the continual Toda equation and the Laplace equation. We obtain a string background associated with a non-trivial solution of the continual Toda equation, which is mapped, under the T-duality transformation, to the hyper-\Kahler Taub-NUT instanton background. It is shown that the integrable property of the non-\Kahlerian spaces have the direct origin in the real heavens: real, self-dual, euclidean, Einstein spaces. The Laplace equation and the continual Toda equation imposed on quasi-\Kahler geometry for consistent string propagation are related to the self-duality conditions of the real heavens with ``translational'' and ``rotational''Killing symmetry respectively.Comment: 21 pages, plain te

Non-commutative M-branes from Open Pure Spinor Supermembrane

Open supermembrane with a constant three-form flux in the pure spinor formalism is examined. The BRST symmetry of the open supermembrane action leads to non-commutative (NC) M-branes. In addition to the NC M5-brane with a self-dual two-form flux, we find a NC M9-brane with an electric flux and a NC M9-brane with a magnetic flux. The former reduces in the critical electric flux limit to an M2-brane on the M9-brane, while the latter reduces in the strong magnetic flux limit to infinitely many Kaluza-Klein monopoles dissolved into the M9-brane. These NC M-branes are shown to preserve a half of 32 supersymmetries.Comment: 17 pages, published versio

A Covariant Approach to Noncommutative M5-branes

We briefly review how to discuss noncommutative (NC) M5-branes and intersecting NC M5-branes from kappa-invariance of an open supermembrane action with constant three-form fluxes. The kappa-invariance gives rise to possible Dirichlet brane configurations. We shortly summarize a construction of projection operators for NC M5-branes and some intersecting configurations of NC M5-branes. A strong flux limit of them is also discussed.Comment: 4 pages, 1 figure, LaTeX, A contribution to Nishinomiya-Yukawa Memorial Symposium on Theoretical Physics ``Noncommutative Geometry and Quantum Spacetime in Physics'' (Nov. 11-15, 2006, Japan). To appear in Progress of Theoretical Physics Supplemen