BPS states for scalar field theories based on $\mathfrak{g}_2$ and $\mathfrak{su}(4)$ algebras

TL;DR

This paper constructs and analyzes BPS solutions in two 1+1 dimensional scalar field models based on the root spaces of the Lie algebras $rak{g}_2$ and $rak{su}(4)$, revealing their solitonic structures.

Contribution

It introduces two novel scalar field models rooted in $rak{g}_2$ and $rak{su}(4)$ Lie algebra structures and explicitly finds their BPS solutions.

Findings

Explicit BPS solutions for both models are obtained.

The models demonstrate rich solitonic structures linked to Lie algebra root systems.

The construction provides new insights into algebraic structures in scalar field theories.

Abstract

We discuss two models in $1+1$ dimensional space-time for real scalar field multiplets on the root space of $\mathfrak{g}_2$ and $\mathfrak{su}(4)$ Lie algebras. The construction of these models is presented and the corresponding BPS solutions are found.