Entanglement entropy and flow in two-dimensional QCD: Parton and string duality

We discuss quantum entanglement between fast and slow degrees of freedom, in a two-dimensional (2D) large Nc gauge theory with Dirac quarks, quantized on the light front. Using the 't Hooft wave functions, we construct the reduced density matrix for an interval in the momentum fraction x space, and calculate its von Neumann entropy in terms of structure functions, that are measured by deep inelastic scattering on mesons (hadrons in general). We found that the entropy is bounded by an area law with logarithmic divergences, proportional to the rapidity of the meson. The evolution of the entanglement entropy with rapidity is fixed by the cumulative singlet parton distribution function (PDF), and bounded from above by a Kolmogorov-Sinai entropy of 1. At low x, the entanglement exhibits an asymptotic expansion, similar to the forward meson-meson scattering amplitude in the Regge limit. The evolution of the entanglement entropy in parton x per unit rapidity measures the meson singlet PDF. The resummed entanglement entropy along the single meson Regge trajectory is stringlike. We suggest that its extension to multimeson states models deep inelastic scattering on a large 2D"nucleus."The result is a large rate of change of the entanglement entropy with rapidity, that matches the current Bekenstein-Bremermann bound for maximum quantum information flow. This mechanism may be at the origin of the large entropy deposition and rapid thermalization, reported in current heavy ion colliders, and may extend to future electron-ion colliders.