The Conformal Penrose Limit and the Resolution of the pp-curvature Singularities

TL;DR

This paper investigates conformal Penrose limits of supergravity solutions with specific geometric structures, revealing supersymmetric plane wave solutions and resolving pp-curvature singularities, with implications for dualities in supergravity theories.

Contribution

It introduces a conformal Penrose limit for solutions with Einstein spaces admitting conformal Killing vectors, resulting in supersymmetric plane wave solutions and singularity resolution in supergravity.

Findings

M^{(0)}_{d} has 1/4 supersymmetry and Virasoro symmetry

The pp-curvature singularity is resolved in D6-brane solutions

Duality between gauged and ungauged supergravity theories is suggested

Abstract

We consider the exact solutions of the supergravity theories in various dimensions in which the space-time has the form M_{d} x S^{D-d} where M_{d} is an Einstein space admitting a conformal Killing vector and S^{D-d} is a sphere of an appropriate dimension. We show that, if the cosmological constant of M_{d} is negative and the conformal Killing vector is space-like, then such solutions will have a conformal Penrose limit: M^{(0)}_{d} x S^{D-d} where M^{(0)}_{d} is a generalized d-dimensional AdS plane wave. We study the properties of the limiting solutions and find that M^{(0)}_{d} has 1/4 supersymmetry as well as a Virasoro symmetry. We also describe how the pp-curvature singularity of M^{(0)}_{d} 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 of Salam and Sezgin on M^{(0)}_{8} and the d=7 ungauged supergravity theory on its pp-wave boundary.