The conformal Penrose limit and the resolution of the pp-curvature singularities

We consider the exact solutions of the supergravity theories in various dimensions in which the spacetime has the form M-d x SD-d where M-d is an Einstein space admitting a conformal Killing vector and SD-d is a sphere of an appropriate dimension. We show that if the cosmological constant of Md is negative and the conformal Killing vector is spacelike, then such solutions will have a conformal Penrose limit. M-d((0)) x SD-d where M-d((0)) is a generalized d-dimensional AdS plane wave. We study the properties of the limiting solutions and find that M-d((0)) has 1/4 supersymmetry as well as a Virasoro symmetry. We also describe how the pp-curvature singularity of M-d((0)) is resolved in the particular case of the D6-branes of D = 10 type IIA supergravity theory. This distinguished case provides an interesting generalization of the plane waves in D = 11 supergravity theory and suggests a duality between the SU(2) gauged d = 8 supergravity theory of Salam and Sezgin on M-8((0)) and the d = 7 ungauged supergravity theory on its pp-wave boundary.