Holographic two-point functions in medium

TL;DR

This paper investigates two-point functions and mutual information in a holographic medium modeled by a generalized p-brane gas, revealing conformal behavior in the extremal limit and the relationship between correlation length and mutual information.

Contribution

It provides a detailed holographic analysis of two-point functions and mutual information in a medium with a generalized p-brane geometry, highlighting conformal properties in the extremal limit.

Findings

Two-point functions decay faster due to medium screening effects.

In the extremal limit, the temporal two-point function remains conformal.

A critical IR distance exists where mutual information vanishes, linked to correlation length.

Abstract

We study two-point correlation function in a medium composed of two kinds of matter, which is the dual of a three-dimensional generalized $p$-brane gas geometry. Following the holographic prescription, we calculate temporal and spatial two-point functions in the medium. In general, the screening effect of the medium makes two-point functions decrease more rapidly than the CFT's two-point function. In the extremal limit, however, we find that a temporal two-point function is still conformal. This indicates that a two-dimensional UV CFT flows into a one-dimensional quantum mechanics in the IR limit. This is consistent with the fact that the near horizon geometry in the extremal limit reduces to AdS$_2$. We also investigate holographic mutual information representing the correlation between two subsystems. We show that a critical distance in the IR region, where the mutual information vanishes, leads to a similar behavior to the correlation length of a two-point function.