Bubbling 1/2 BPS Geometries and Penrose Limits

TL;DR

This paper explores how to perform Penrose limits on bubbling 1/2 BPS geometries, deriving the pp-wave geometry with corrections directly from the original AdS_5 x S^5 setup, including configurations with concentric rings.

Contribution

It provides a method to obtain the Penrose limit of bubbling geometries at the level of a single function z, including 1/R^2 corrections, and applies it to concentric ring configurations.

Findings

Successfully derived the pp-wave with 1/R^2 corrections from bubbling geometries.

Demonstrated the Penrose limit process at the function level z.

Extended the analysis to concentric ring configurations.

Abstract

We discuss how to take a Penrose limit in bubbling 1/2 BPS geometries at the stage of a single function z(x_1,x_2,y). By starting from the z of the AdS_5 x S^5 we can directly derive that of the pp-wave via the Penrose limit. In that time the function z for the pp-wave with 1/R^2-corrections is obtained. We see that it surely reproduces the pp-wave with 1/R^2 terms. In addition we consider the Penrose limit in the configuration of the concentric rings.