# Entanglement branes in a two-dimensional string theory

## Abstract

What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. Here, we derive the modular Hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an entanglement brane, or E-brane.

- Authors:

- Univ. of California, Santa Barbara, CA (United States). Dept. of Physics
- Univ. of Virginia, Charlottesville, VA (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Univ. of California, Santa Barbara, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1424734

- Grant/Contract Number:
- SC0011702

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 9; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N Expansion; D-branes; Topological Field Theories; Topological Strings

### Citation Formats

```
Donnelly, William, and Wong, Gabriel.
```*Entanglement branes in a two-dimensional string theory*. United States: N. p., 2017.
Web. doi:10.1007/JHEP09(2017)097.

```
Donnelly, William, & Wong, Gabriel.
```*Entanglement branes in a two-dimensional string theory*. United States. doi:10.1007/JHEP09(2017)097.

```
Donnelly, William, and Wong, Gabriel. Wed .
"Entanglement branes in a two-dimensional string theory". United States.
doi:10.1007/JHEP09(2017)097. https://www.osti.gov/servlets/purl/1424734.
```

```
@article{osti_1424734,
```

title = {Entanglement branes in a two-dimensional string theory},

author = {Donnelly, William and Wong, Gabriel},

abstractNote = {What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. Here, we derive the modular Hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an entanglement brane, or E-brane.},

doi = {10.1007/JHEP09(2017)097},

journal = {Journal of High Energy Physics (Online)},

number = 9,

volume = 2017,

place = {United States},

year = {Wed Sep 20 00:00:00 EDT 2017},

month = {Wed Sep 20 00:00:00 EDT 2017}

}