# Entanglement in Regge scattering using the AdS/CFT correspondence

## Abstract

The eikonalized parton-parton scattering amplitude at large √s and large impact parameter, is dominated by the exchange of a hyperbolic surface in walled AdS. Its analytical continuation yields a world sheet instanton that is at the origin of the Reggeization of the amplitude and a thermallike quantum entropy S_{T}. We explicitly construct the entangled density matrix following from the exchanged surface, and show that its von-Neumann entanglement entropy S_{E} coincides with the thermallike entropy, i.e., S_{T} = S_{E}. The ratio of the entanglement entropy to the transverse growth of the exchanged surface is similar to the Bekenstein entropy ratio for a black hole, with a natural definition of saturation and the on-set of chaos in high energy collisions. The largest eigenvalues of the entangled density matrix obey a cascade equation in rapidity, reminiscent of nonlinear QCD evolution of wee-dipoles at low-x and weak coupling. We suggest that the largest eigenvalues describe the probability distributions of wee-quanta at low-x and strong coupling that maybe measurable at present and future pp and ep colliders.

- Authors:

- Publication Date:

- Research Org.:
- Stony Brook Univ., Stony Brook, NY (United States); State Univ. of New York (SUNY), Albany, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1547965

- Alternate Identifier(s):
- OSTI ID: 1610117

- Grant/Contract Number:
- FG02-88ER40388

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 4; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; astronomy & astrophysics; physics; entanglement in field theory; gauge-gravity dualities; nonperturbative effects in field theory; scattering amplitudes

### Citation Formats

```
Liu, Yizhuang, and Zahed, Ismail. Entanglement in Regge scattering using the AdS/CFT correspondence. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.046005.
```

```
Liu, Yizhuang, & Zahed, Ismail. Entanglement in Regge scattering using the AdS/CFT correspondence. United States. doi:10.1103/PhysRevD.100.046005.
```

```
Liu, Yizhuang, and Zahed, Ismail. Tue .
"Entanglement in Regge scattering using the AdS/CFT correspondence". United States. doi:10.1103/PhysRevD.100.046005.
```

```
@article{osti_1547965,
```

title = {Entanglement in Regge scattering using the AdS/CFT correspondence},

author = {Liu, Yizhuang and Zahed, Ismail},

abstractNote = {The eikonalized parton-parton scattering amplitude at large √s and large impact parameter, is dominated by the exchange of a hyperbolic surface in walled AdS. Its analytical continuation yields a world sheet instanton that is at the origin of the Reggeization of the amplitude and a thermallike quantum entropy ST. We explicitly construct the entangled density matrix following from the exchanged surface, and show that its von-Neumann entanglement entropy SE coincides with the thermallike entropy, i.e., ST = SE. The ratio of the entanglement entropy to the transverse growth of the exchanged surface is similar to the Bekenstein entropy ratio for a black hole, with a natural definition of saturation and the on-set of chaos in high energy collisions. The largest eigenvalues of the entangled density matrix obey a cascade equation in rapidity, reminiscent of nonlinear QCD evolution of wee-dipoles at low-x and weak coupling. We suggest that the largest eigenvalues describe the probability distributions of wee-quanta at low-x and strong coupling that maybe measurable at present and future pp and ep colliders.},

doi = {10.1103/PhysRevD.100.046005},

journal = {Physical Review D},

number = 4,

volume = 100,

place = {United States},

year = {2019},

month = {8}

}

DOI: 10.1103/PhysRevD.100.046005

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