Entanglement, Trace Anomaly and Confinement in QCD

We formulate confinement in 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 $c_h = 8π^2 R_{EE}^2,ρ_h(R_{EE})$ and a mechanical entropy $S_{EE}(y)=c_h,y$ that grows linearly with rapidity $y$. The entropy gradient $\partial_R S_{EE}$ 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 $Σ_\perp = S^2_{R_{EE}}$ (which, in the infinite-momentum frame, 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 ($y\to 0$). Imposing unitarity on an entropic ansatz for the amplitude yields $σ(s)\propto y^δ$. 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 non-perturbative QCD inputs, unifying the trace anomaly, entanglement entropy, and high-energy scattering within a single quantitative framework.

💡 Research Summary

The paper proposes a novel, entropy‑based picture of confinement in quantum chromodynamics (QCD) that complements the traditional Wilson loop area‑law criterion. The authors argue that quark and gluon quantum information is not spread throughout space but is instead localized on a transverse two‑dimensional entangling surface – a sphere of radius (R_{EE}) – which they call the “information wall.” This radius is not a phenomenological parameter; it is extracted from lattice QCD calculations of the scalar (trace) gravitational form factors (GFFs) for quarks and gluons. By Fourier‑transforming the GFFs to impact‑parameter space, they obtain a two‑dimensional trace‑anomaly density (\rho_h(b_\perp)). The radius (R_{EE}) is defined as the point where (\rho_h(b_\perp)) reaches its maximum, and the corresponding density (\rho_h(R_{EE})) together with (R_{EE}) fixes a dimensionless slope \