A Universal Behavior of Half BPS Probes in the Superstar Ensemble

Abstract

In this paper we probe the typical states of the superstar ensemble of (hep-th/0508023) using half-BPS states of type-IIB string theory on AdS$_5 \times$ S$^5$. We find a very simple universal result that has the structure $\log\, \lag\lag \y \; \y \rag\rag_\calo \approx \a\, h \, \log N$, where $h$ is the conformal weight of the probe $\y$ and $\a$ is a constant that depends mainly of the shape of the probe $\y$. A complete understanding of some properties of this leading term from the dual effective superstar geometry point of view is still lacking.