Gluon Saturation and Black Hole Criticality

TL;DR

The paper investigates a proposed link between the onset of non-linear saturation effects in high-energy QCD and critical phenomena in gravitational collapse. It argues that holography requires continuous self-similarity, realized in the spherical collapse of a perfect fluid, to map QCD saturation (geometric scaling) onto gravitational dynamics. The authors show that the Choptuik exponent in five dimensions closely matches the QCD saturation exponent in the traceless energy-momentum tensor limit, strengthening the gauge/gravity correspondence for high-density QCD. This work suggests a deeper, scale-invariant connection between parton saturation and black hole formation, with potential implications for understanding non-linear QCD dynamics via gravitational analogs.

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.

Figures (8)

• Figure 1: The two relevant bulk geometries for confinement / deconfinement transition.
• Figure 2: The dependence on $x$ of the proton structure function $F_2$ for different values of $Q{}^{2}$.
• Figure 3: QCD kinematic space in DIS
• Figure 4: BFKL gluon cascade in multi--Regge kinematics
• Figure 5: Continuous self--similarity on the $(Y, \log Q{}^{2})$ plane.