Penrose Limits of Orbifolds and Orientifolds

TL;DR

This paper investigates the Penrose limits of various orbifolds and orientifolds of AdS spaces, revealing the resulting wave geometries, their singularities, and possible resolutions, with applications to string theory and supergravity backgrounds.

Contribution

It provides a detailed analysis of the Penrose limits of orbifolds and orientifolds in AdS spaces, including singularity resolution and embeddings in flat space, extending previous work on pp-wave geometries.

Findings

Penrose limits produce wave geometries with orbifold singularities.

Desingularization leads to asymptotically locally pp-wave backgrounds.

Certain singularities can be resolved by gravitational instantons.

Abstract

We study the Penrose limit of various AdS_p X S^q orbifolds. The limiting spaces are waves with parallel rays and singular wave fronts. In particular, we consider the orbifolds AdS_3 X S^3/\Gamma, AdS_5 X S^5/\Gamma and AdS_{4,7} X S^{7,4}/\Gamma where \Gamma acts on the sphere and/or the AdS factor. In the pp-wave limit, the wave fronts are the orbifolds C^2/\Gamma, C^4/\Gamma and R XC^4/\Gamma, respectively. When desingularization is possible, we get asymptotically locally pp-wave backgrounds (ALpp). The Penrose limit of orientifolds are also discussed. In the AdS_5 X RP^5 case, the limiting singularity can be resolved by an Eguchi-Hanson gravitational instanton. The pp-wave limit of D3-branes near singularities in F-theory is also presented. Finally, we give the embedding of D-dimensional pp-waves in flat M^{2,D} space.