Kink-kink solutions in BPS impurity models

TL;DR

This paper demonstrates that BPS-impurity theories can support degenerate kink-kink solutions at any distance, using singular impurities in sine-Gordon and $^6$ models, revealing new static solutions and spectral properties.

Contribution

It introduces the existence of BPS kink-kink solutions supported by singular impurities in specific models, a novel finding in impurity theory.

Findings

Existence of degenerate kink-kink solutions at arbitrary distances.

Solutions match known double sine-Gordon and Christ-Lee kinks.

Spectral analysis shows modes with odd nodes to cancel impurity singularity.

Abstract

We show that BPS-impurity theories may support BPS kink-kink solutions i.e., an energetically degenerated family of solutions describing two kinks at any mutual distance. This requires a singular impurity. As an example we consider the sine-Gordon and $\phi^6$ models coupled with such a BPS impurity. Interestingly, obtained solutions are identical to double sine-Gordon kinks and Christ-Lee kinks respectively. We also study the spectral flow on the moduli space. All the modes have an odd number of nodes to cancel the singularity of the impurity.