The Conformal Penrose Limit: Back to Square One

Abstract

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.

arXiv comment16 pages, LaTeX

References in corpus (16)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• Penrose limits and maximal supersymmetry
• The domain-wall/QFT correspondence
• Sasaki-Einstein Manifolds and Volume Minimisation
• Macroscopic superstrings as interpolating solitons
• Supergravity on the Brane
• Kaluza-Klein Consistency, Killing Vectors, and Kahler Spaces
• Interpretation of the Siklos solutions as exact gravitational waves in the anti-de Sitter universe
• On Domain-Wall/QFT Dualities in Various Dimensions
• Cones, Tri-Sasakian Structures and Superconformal Invariance
• AdS/CFT in the Infinite Momentum Frame
• Branes, AdS gravitons and Virasoro symmetry
• Randall-Sundrum Zero Mode as a Penrose Limit
• Vanishing Scalar Invariant Spacetimes in Supergravity
• The Conformal Penrose Limit and the Resolution of the pp-curvature Singularities