Entanglement, trace anomaly, and confinement in QCD
We formulate confinement in quantum chromodynamics (QCD) as an entropic surface phenomenon. Quark and gluon quantum information is localized on a transverse, entangling two-sphere of radius 𝑅 𝐸𝐸 ; at this radius the QCD vacuum—partitioned by a hadron into interior and exterior regions—reaches its maximal entanglement entropy. Lattice-QCD determinations of the scalar (trace) gravitational form factors fix both 𝑅 𝐸𝐸 and the transverse trace-anomaly density 𝜌 ℎ (𝑅 𝐸𝐸 ), yielding a parameter-free slope 𝑐 ℎ = 8𝜋 2 𝑅𝑆$^2_{𝐸𝐸}$𝜌 ℎ (𝑅 𝐸𝐸 ) and a mechanical entropy 𝑆 𝐸𝐸 (𝑦) = 𝑐 ℎ 𝑦 that grows linearly with rapidity 𝑦. The entropy gradient ∂ 𝑅 𝑆 𝐸𝐸 changes sign at 𝑅 𝐸𝐸 : it pushes colored degrees of freedom outward for 𝑟 <𝑅 𝐸𝐸 and pulls them inward for 𝑟 >𝑅 𝐸𝐸 , thereby localizing them on the codimension-2 entangling two-sphere Σ ⊥ = 𝑆$^2_{𝑅_{𝐸𝐸}}$ (which, in the infinite-momentum frame (IMF), projects onto the transverse plane)—the “information wall.” This provides a high-energy (large-𝑦) entropic confinement diagnostic that complements—rather than replaces—Wilson’s area-law criterion, which probes long-distance dynamics near the rest frame (𝑦 → 0). Imposing unitarity on an entropic ansatz for the amplitude yields 𝜎(𝑠) ∝ 𝑦 𝛿 . World data favor 𝛿 = 2 for elastic 𝑝𝑝($𝑝\bar{𝑝}$) scattering and heavy-quark photoproduction, whereas 𝜙 photoproduction favors a softer 𝛿 = 0.387. All extracted cross sections remain well below the Froissart-Martin bound. These results provide a confinement criterion quantified directly from nonperturbative QCD inputs, unifying the trace anomaly, entanglement entropy, and high-energy scattering within a single quantitative framework.