The Conformal Penrose Limit: Back to Square One

We show that the conformal Penrose limit is an ordinary plane wave limit in a higher dimensional framework which resolves the spacetime singularity. The higher dimensional framework is provided by Ricci-flat manifolds which are of the form M_D = M_d x B, where M_d is an Einstein spacetime that has a negative cosmological constant and admits a spacelike conformal Killing vector, and B is a complete Sasaki-Einstein space with constant sectional curvature. We define the Kaluza-Klein metric of M_D through the conformal Killing potential of M_d and prove that M_d has a conformal Penrose limit if and only if M_D has an ordinary plane wave limit. Further properties of the limit are discussed.