Entanglement, Trace Anomaly and Confinement in QCD

Abstract

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 ${\rho }_h(R_{EE})$, yielding a parameter-free slope $c_h=8{\pi }^2{R}_{EE}^2{\rho }_h(R_{EE})$ 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 ${\Sigma }_{\perp }=S_{R_{EE}}^2$ (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 $\sigma (s)\propto y^{\delta }$. World data favor $\delta =2$ for elastic $pp(p\bar{p})$ scattering and heavy-quark photoproduction, whereas $\varphi$ photoproduction favors a softer $\delta =0.387$. 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.

v4: published version to Physical Review D (Letter)

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