# A note on entanglement edge modes in Chern Simons theory

## Abstract

We elaborate on the extended Hilbert space factorization of Chern Simons theory and show how this arises naturally from a proper regularization of the entangling surface in the Euclidean path integral. The regularization amounts to stretching the entangling surface into a co-dimension one surface which hosts edge modes of the Chern Simons theory when quantized on a spatial subregion. The factorized state is a regularized Ishibashi state and reproduces the well known topological entanglement entropies. We illustrate how the same factorization arises from the gluing of two spatial subregions via the entangling product defined by Donnelly and Freidel.

- Authors:

- Univ. of Virginia, Charlottesville, VA (United States). Dept. of Physics; Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)

- Publication Date:

- Research Org.:
- US Department of the Navy, Charleston, SC (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1545021

- Grant/Contract Number:
- [SC0007894]

- Resource Type:
- Accepted Manuscript

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

- Additional Journal Information:
- [Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 8]; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chern-Simons Theories; Conformal Field Theory; Topological Field Theories; Topological Strings

### Citation Formats

```
Wong, Gabriel. A note on entanglement edge modes in Chern Simons theory. United States: N. p., 2018.
Web. doi:10.1007/jhep08(2018)020.
```

```
Wong, Gabriel. A note on entanglement edge modes in Chern Simons theory. United States. doi:10.1007/jhep08(2018)020.
```

```
Wong, Gabriel. Tue .
"A note on entanglement edge modes in Chern Simons theory". United States. doi:10.1007/jhep08(2018)020. https://www.osti.gov/servlets/purl/1545021.
```

```
@article{osti_1545021,
```

title = {A note on entanglement edge modes in Chern Simons theory},

author = {Wong, Gabriel},

abstractNote = {We elaborate on the extended Hilbert space factorization of Chern Simons theory and show how this arises naturally from a proper regularization of the entangling surface in the Euclidean path integral. The regularization amounts to stretching the entangling surface into a co-dimension one surface which hosts edge modes of the Chern Simons theory when quantized on a spatial subregion. The factorized state is a regularized Ishibashi state and reproduces the well known topological entanglement entropies. We illustrate how the same factorization arises from the gluing of two spatial subregions via the entangling product defined by Donnelly and Freidel.},

doi = {10.1007/jhep08(2018)020},

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

number = [8],

volume = [2018],

place = {United States},

year = {2018},

month = {8}

}

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