# Entanglement Entropy in Integrable Field Theories with Line Defects I. Topological Defect

## TL;DR

This paper investigates how purely transmissive topological line defects influence entanglement entropy in 1+1 dimensional integrable quantum field theories, revealing they do not alter UV entropy but slightly modify IR corrections.

## Contribution

It demonstrates that topological defects do not impact UV entanglement entropy and only slightly modify IR corrections, using the form factor bootstrap method.

## Key findings

- Topological defects do not affect UV entanglement entropy.
- Topological defects cause slight modifications in IR exponential corrections.
- Results hold for both unitary and non-unitary theories.

## Abstract

In this paper and a companion one, we study the effect of integrable line defects on entanglement entropy in massive integrable field theories in 1+1 dimensions. The current paper focuses on topological defects that are purely transmissive. Using the form factor bootstrap method, we show that topological defects do not affect the the entanglement entropy in the UV limit and modify slightly the leading exponential correction in the IR. This conclusion holds for both unitary and non-unitary field theories. In contrast, non-topological defects affect the entanglement entropy more significantly both in UV and IR limit and will be studied in the companion paper.