TY - JOUR
T1 - Rapidity evolution of the entanglement entropy in quarkonium
T2 - Parton and string duality
AU - Liu, Yizhuang
AU - Nowak, MacIej A.
AU - Zahed, Ismail
N1 - Publisher Copyright:
© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
PY - 2022/6/1
Y1 - 2022/6/1
N2 - We investigate the quantum entanglement in rapidity space of the soft gluon wave function of a quarkonium in theories with nontrivial rapidity evolutions. We found that the rapidity evolution drastically changes the behavior of the entanglement entropy, at any given order in perturbation theory. At large Nc, the reduced density matrices that "resum"the leading rapidity logs can be explicitly constructed, and shown to satisfy Balitsky-Kovchegov-like evolution equations. We study their entanglement entropy in a simplified 1+1 toy model and in 3D QCD. The entanglement entropy in these cases, after resummation, is shown to saturate the Kolmogorov-Sinai bound of 1. Remarkably, in 3D QCD the essential growth rate of the entanglement entropy is found to vanish at large rapidities, a result of kinematical "quenching"in transverse space. The one-body reduction of the entangled density matrix obeys a Balitsky-Fadin-Kuraev-Lipatov evolution equation, which can be recast as an evolution in an emergent AdS space, at large impact parameter and large rapidity. This observation allows the extension of the perturbative wee parton evolution at low x, to a dual nonperturbative evolution of string bits in curved AdS5 space, with manifest entanglement entropy in the confining regime.
AB - We investigate the quantum entanglement in rapidity space of the soft gluon wave function of a quarkonium in theories with nontrivial rapidity evolutions. We found that the rapidity evolution drastically changes the behavior of the entanglement entropy, at any given order in perturbation theory. At large Nc, the reduced density matrices that "resum"the leading rapidity logs can be explicitly constructed, and shown to satisfy Balitsky-Kovchegov-like evolution equations. We study their entanglement entropy in a simplified 1+1 toy model and in 3D QCD. The entanglement entropy in these cases, after resummation, is shown to saturate the Kolmogorov-Sinai bound of 1. Remarkably, in 3D QCD the essential growth rate of the entanglement entropy is found to vanish at large rapidities, a result of kinematical "quenching"in transverse space. The one-body reduction of the entangled density matrix obeys a Balitsky-Fadin-Kuraev-Lipatov evolution equation, which can be recast as an evolution in an emergent AdS space, at large impact parameter and large rapidity. This observation allows the extension of the perturbative wee parton evolution at low x, to a dual nonperturbative evolution of string bits in curved AdS5 space, with manifest entanglement entropy in the confining regime.
UR - https://www.scopus.com/pages/publications/85134264021
U2 - 10.1103/PhysRevD.105.114028
DO - 10.1103/PhysRevD.105.114028
M3 - Article
AN - SCOPUS:85134264021
SN - 2470-0010
VL - 105
JO - Physical Review D
JF - Physical Review D
IS - 11
M1 - 114028
ER -