# Form factors in the presence of integrable defects

## TL;DR

This paper develops a framework for calculating form factors in two-dimensional integrable defect theories, expressing bulk operator form factors via transmission factors and explicitly computing defect operator form factors for specific models.

## Contribution

It introduces form factor axioms for defect theories, relates bulk form factors to transmission factors, and presents a fusion method for boundary form factors, advancing the understanding of integrable defect models.

## Key findings

- Explicit form factors for free boson and Lee-Yang models
- Form factor axioms for defect operators established
- Fusion method for boundary form factors demonstrated

## Abstract

Form factor axioms are derived in two dimensional integrable defect theories for matrix elements of operators localized both in the bulk and on the defect. The form factors of bulk operators are expressed in terms of the bulk form factors and the transmission factor. The structure of the form factors of defect operators is established in general, and explicitly calculated in particular, for the free boson and for some operator of the Lee-Yang model. Fusion method is also presented to generate boundary form factor solutions for a fused boundary from the known unfused ones.