# Solvable self-dual impurity models

## TL;DR

This paper introduces a family of self-dual impurity models with exactly solvable BPS sectors, providing analytical insights into their moduli space, symmetries, and vibrational properties across different topological sectors.

## Contribution

It presents a novel class of self-dual impurity models with exactly solvable BPS sectors and analytical characterization of their moduli space and symmetries.

## Key findings

- Exact metric on moduli space derived analytically
- Generalized translational symmetry explicitly formulated
- Vibrational modes analyzed across topological sectors

## Abstract

We find a family of (half) self-dual impurity models such that the self-dual (BPS) sector is exactly solvable, for any spatial distribution of the impurity, both in the topologically trivial case and for kink (or antikink) configurations. This allows us to derive the metric on the corresponding one-dimensional moduli space in an analytical form. Also the generalized translational symmetry is found in an exact form. This symmetry provides a motion on moduli space which transforms one BPS solution into another. Finally, we analyse exactly how vibrational properties (spectral modes) of the BPS solutions depend on the actual position on moduli space. These results are obtained both for the nontrivial topological sector (kinks or antikinks) as well as for the topologically trivial sector, where the motion on moduli space represents a kink-antikink annihilation process.