\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
In this paper we classify the ten dimensional half BPS solutions of the
type IIB supergravity which have $SO(4)\times SO(4)\times U(1)$ 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: {\it 1)} those with $R\times S^3$ boundary and {\it 2)} those
with one dimensional light-like boundary. Each class can be divided into
some subclasses depending on asymptotic characteristics of the solutions.
We analyze each of these classes in some detail
and elaborate on their dual gauge theory description, the corresponding
$2d$ fermion picture and matrix Chern-Simons theory as the effective
theory of the half BPS spherical threebrane probes.
\end{document}