# Conformal interfaces between free boson orbifold theories

## TL;DR

This paper constructs and analyzes a broad class of conformal interfaces between free boson orbifold theories, revealing their fusion properties and symmetry-related features in two-dimensional conformal field theories.

## Contribution

It introduces a systematic method to construct and classify conformal interfaces between c=1 theories and their orbifolds, including their fusion and symmetry properties.

## Key findings

- Computed fusion products for all constructed defects
- Identified invertible topological interfaces linked to symmetries
- Mapped untwisted sectors of orbifolds to parent theories

## Abstract

We construct a large class of conformal interfaces between two-dimensional c=1 conformal field theories describing compact free bosons and their Z_2 orbifolds. The interfaces are obtained by constructing boundary states in the corresponding c=2 product theories and applying the unfolding procedure. We compute the fusion products for all of these defects, and identify the invertible topological interfaces associated to global symmetries, the interfaces corresponding to marginal deformations, and the interfaces which map the untwisted sector of an orbifold to the invariant states of the parent theory.