Entanglement entropy and flow in two dimensional QCD: parton and string duality

TL;DR

This paper explores quantum entanglement in a 2D large N_c gauge theory, linking entanglement entropy evolution to parton distributions and string-like behavior, with implications for understanding entropy production in high-energy collisions.

Contribution

It introduces a novel connection between entanglement entropy, parton distributions, and string duality in 2D QCD, providing a new perspective on quantum information flow in hadronic processes.

Findings

Entanglement entropy is bounded by an area law with logarithmic divergences.

The entropy evolution is governed by the meson singlet PDF and is string-like along Regge trajectories.

The entropy change rate matches the Bekenstein-Bremermann bound, suggesting a link to entropy production in heavy ion collisions.

Abstract

We discuss quantum entanglement between fast and slow degrees of freedom, in a two dimensional (2D) large $N_c$ 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 DIS 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 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 re-summed entanglement entropy along the single meson Regge trajectory, is string-like. We suggest that its extension to multi-meson states, models DIS scattering on a large 2D $^\prime$nucleus$^\prime$. 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.