On the smoothness of multi-M2 brane horizons

We calculate the degree of horizon smoothness of multi- $M2$-brane solution with branes along a common axis. We find that the metric is generically only thrice continuously differentiable at any of the horizons. The four-form field strength is found to be only twice continuously differentiable. We work with Gaussian null-like co-ordinates which are obtained by solving geodesic equations for multi-$M2$ brane geometry. We also find different, exact co-ordinate transformations which take the metric from isotropic co-ordinates to co-ordinates in which metric is thrice differentiable at the horizon. Both methods give the same result that the multi-$M2$ brane metric is only thrice continuously differentiable at the horizon.Comment: 24 pages, reference added, modified equation for non-singularity of metri

An example of localized D-branes solution on PP-wave backgrounds

In this note we provide an explicit example of type IIB supersymmetric D3-branes solution on a pp-wave like background, consisting in the product of an eight-dimensional pp-wave times a two-dimensional flat space. An interesting property of our solution is the fully localization of the D3-branes (i.e. the solution depends on all the transverse coordinates). Then we show the generalization to other Dp-branes and to the D1/D5 system.Comment: 14 pages, 1 table; v2. references adde