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 $r R_{EE}$, thereby localizing them on the codimension-2 entangling two-sphere $\Sigma_\perp = S^2_{R_{EE}}$ (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 $\sigma(s)\propto y^{\delta}$. World data favor $\delta=2$ for elastic $pp\,(p\bar p)$ scattering and heavy-quark photoproduction, whereas $\phi$ 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.