[Paper Review] Classicalization and unitarization of wee partons in QCD and Gravity: The CGC-Black Hole correspondence

Gia Dvali, Raju Venugopalan|arXiv (Cornell University)|Jun 22, 2021

Black Holes and Theoretical PhysicsPhysics and Astronomy104 references39 citations

TL;DR

This paper proposes a deep correspondence between Color Glass Condensates (CGCs) in high-energy QCD and black holes in gravity, showing that both systems exhibit classicalization and unitarization of 'wee partons' via critical packing of soft gluons or gravitons. The key result is that both systems saturate a universal entropy bound Smax = 1/α(QS), with entropy equal to the area in units of a Goldstone scale—yielding Bekenstein-Hawking-like entropy in gravity and a similar area-law in QCD.

ABSTRACT

We discuss a remarkable correspondence between the description of Black Holes as highly occupied condensates of $N$ weakly interacting gravitons and that of Color Glass Condensates (CGCs) as highly occupied gluon states. In both cases, the dynamics of "wee partons" in Regge asymptotics is controlled by emergent semi-hard scales that lead to perturbative unitarization and classicalization of $2 ightarrow N$ particle amplitudes at weak coupling. In particular, they attain a maximal entropy permitted by unitarity, bounded by the inverse coupling $\alpha$ of the respective constituents. Strikingly, this entropy is equal to the area measured in units of the Goldstone constant corresponding to the spontaneous breaking of Poincar{\'{e}} symmetry by the corresponding graviton or gluon condensate. In gravity, the Goldstone constant is the Planck scale, and gives rise to the Bekenstein-Hawking entropy. Likewise, in the CGC, the corresponding Goldstone scale is determined by the onset of gluon screening. We point to further similarities in Black Hole formation, thermalization and decay, to that of the Glasma matter formed from colliding CGCs in ultrarelativistic nuclear collisions, which decays into a Quark-Gluon Plasma.

Motivation & Objective

• To establish a correspondence between high-energy QCD's Color Glass Condensate (CGC) and black hole physics in gravity.
• To show that both systems exhibit classicalization and perturbative unitarization of 2→N amplitudes in the Regge limit.
• To demonstrate that maximal entropy in both systems is bounded by Smax = 1/α(QS), linked to emergent semi-hard scales.
• To unify the description of black hole formation and Glasma formation in ultrarelativistic heavy-ion collisions via shared universal dynamics.

Proposed method

• Proposes a correspondence between the CGC (highly occupied gluon state) and black holes (highly occupied graviton condensate) in the Regge limit.
• Uses the critical packing condition N = 1/α(QS) to define saturation of soft parton states.
• Applies the entropy bound Smax = 1/α(QS) derived from unitarity, linking it to area in units of a Goldstone scale f.
• Identifies the Goldstone scale f as the Planck scale in gravity and the gluon screening scale in QCD.
• Analyzes 2→N scattering amplitudes in the multi-Regge kinematics, showing exponential suppression e−N compensates degeneracy eN.
• Uses effective field theories and eikonalization to unitarize amplitudes at the scale RS = 1/QS.

Experimental results

Research questions

• RQ1 How do CGCs in QCD and black holes in gravity both achieve classicalization and unitarization of 2→N amplitudes in the Regge limit?
• RQ2 What is the origin of the universal entropy bound Smax = 1/α(QS) in both systems, and how is it related to area and Goldstone modes?
• RQ3 Why do both CGC and black hole systems saturate the same entropy bound, and what does this imply about their universal dynamics?
• RQ4 How is the Glasma state formed in heavy-ion collisions analogous to black hole formation in terms of dynamics and thermalization?
• RQ5 What role does spontaneous Poincaré symmetry breaking play in generating the Goldstone scale f that determines the entropy in both systems?

Key findings

• The maximal entropy Smax = 1/α(QS) is saturated in both CGC and black hole systems, representing a universal unitarity bound.
• Entropy is proportional to area in units of the Goldstone scale f, yielding Smax = Area × f², with f = MP in gravity and f = Qs in QCD.
• The saturation momentum QS defines a de Broglie wavelength RS = 1/QS, at which the system becomes classical and unitary.
• The 2→N scattering amplitude for soft partons is unitarized via eikonalization, with exponential suppression e−N balancing the degeneracy eN of microstates.
• The typical final-state momentum |p| ∼ MP/√s = 1/RS matches the Hawking temperature and Schwarzschild radius, linking dynamics to black hole thermodynamics.
• The correspondence extends to decay, thermalization, and information recovery, suggesting universal behavior in saturated systems.