Gluon Saturation and Black Hole Criticality

TL;DR

This paper explores the deep connection between gluon saturation in high energy QCD and black hole critical phenomena, highlighting the role of continuous self-similarity and geometric scaling in this correspondence.

Contribution

It introduces the importance of continuous self-similarity in mapping gauge theory to gravity, linking geometric scaling in DIS data to black hole criticality.

Findings

Critical anomalous dimension matches black hole critical exponent.

Continuous self-similarity is essential for the gauge-gravity correspondence.

Choptuik exponent approaches QCD critical value in specific limits.

Abstract

We discuss the recent proposal in hep-th/0611312 where it was shown that the critical anomalous dimension associated to the onset of non-linear effects in the high energy limit of QCD coincides with the critical exponent governing the radius of the black hole formed in the spherically symmetric collapse of a massless scalar field. We argue that a new essential ingredient in this mapping between gauge theory and gravity is continuous self-similarity, not present in the scalar field case but in the spherical collapse of a perfect fluid with barotropic equation of state. We identify this property with geometric scaling, present in DIS data at small values of Bjorken x. We also show that the Choptuik exponent in dimension five tends to the QCD critical value in the traceless limit of the energy momentum tensor.