Extended multi-scalar field theories in (1+1) dimensions

TL;DR

This paper constructs new multi-scalar field theories in (1+1) dimensions supporting BPS kink solutions, using the extension method to derive models with coupled scalar fields and analyzing their stability.

Contribution

It introduces a systematic way to build multi-scalar theories with BPS solutions from known one-scalar models using the extension method.

Findings

Explicit multi-scalar models with BPS solutions are constructed.

Original BPS solutions remain solutions in the multi-scalar models.

Linear stability of the solutions is analyzed.

Abstract

We present the explicit construction of some multi-scalar field theories in (1+1) dimensions supporting BPS (Bogomol'nyi--Prasad--Sommerfield) kink solutions. The construction is based on the ideas of the so-called extension method. In particular, several new interesting two-scalar and three-scalar field theories are explicitly constructed from non-trivial couplings between well-known one-scalar field theories. The BPS solutions of the original one-field systems will be also BPS solutions of the multi-scalar system by construction, and therefore we will analyse their linear stability properties for the constructed models.