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

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.