A Universal Behavior of Half BPS Probes in the Superstar Ensemble

TL;DR

This paper uncovers a universal logarithmic behavior in the correlation functions of half-BPS probes within the superstar ensemble of type-IIB string theory on AdS5×S5, revealing a simple structure dependent on probe shape and conformal weight.

Contribution

It demonstrates a universal logarithmic pattern in correlators of half-BPS states across the superstar ensemble, highlighting a simple dependence on probe properties.

Findings

Correlation functions scale as log N with a coefficient depending on probe shape.

Universal behavior observed across different probe configurations.

Highlights gaps in understanding from the dual geometry perspective.

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.