# A note on entanglement edge modes in Chern Simons theory

## TL;DR

This paper explores the natural emergence of edge modes and Hilbert space factorization in Chern-Simons theory through a regularized entangling surface, connecting topological entanglement entropy with boundary states.

## Contribution

It demonstrates how a proper regularization of the entangling surface leads to a natural factorization involving edge modes and reproduces known topological entanglement entropies.

## Key findings

- Edge modes arise from regularized entangling surface
- Factorized state is a regularized Ishibashi state
- Reproduces topological entanglement entropy

## 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 glueing of two spatial subregions via the entangling product defined by Donnelly and Freidel.