On Classification Of The Bubbling Geometries

TL;DR

This paper classifies all ten-dimensional half BPS solutions in type IIB supergravity with specific symmetries, analyzing their structure and dual gauge theories, especially the Matrix Chern-Simons theory.

Contribution

It provides a comprehensive classification of LLM geometries based on asymptotic and causal properties, linking them to dual gauge theories and effective probe descriptions.

Findings

Classified solutions into two main boundary types.

Connected geometries to Matrix Chern-Simons theory.

Elaborated on dual gauge theory descriptions.

Abstract

In this paper we classify the ten dimensional half BPS solutions of the type IIB supergravity which have SO(4) X SO(4) X U(1) isometry found by Lin-Lunin-Maldacena (LLM). Our classification is based on their asymptotic behavior and causal structure according which they fall into two classes: 1) those with R X S^3 boundary and 2) those with one dimensional light-like boundary. Each class can be divided into some subclasses depending on the asymptotic characteristics of the solutions, which in part specify the global charges defining the geometry. We analyze each of these classes in some detail and elaborate on their dual gauge theory description. In particular, we show that the Matrix Chern-Simons theory which is the gauge theory dual to the LLM geometries, can be obtained as the effective theory of spherical threebrane probes in the half BPS sector.