BPS Sphalerons in the $F_2$ Non-Linear Sigma Model

TL;DR

This paper constructs and analyzes static and time-dependent solutions, including BPS sphalerons, in the $F_2$ non-linear sigma model on four-dimensional Minkowski space, revealing their energy bounds and properties.

Contribution

It provides explicit analytical solutions and explores their properties in the $F_2$ non-linear sigma model, including static BPS solutions and their time-dependent counterparts.

Findings

Static solutions saturate an energy lower bound.

Solutions can be derived from coupled first order equations.

Time-dependent solutions exhibit specific dynamic properties.

Abstract

We construct static and also time-dependent solutions in a non-linear sigma model with target space being the flag manifold $F_2=SU(3)/U(1)^2$ on the four dimensional Minkowski space-time by analytically solving the second order Euler-Lagrange equation. We show the static solutions saturate an energy lower bound and can be derived from coupled first order equations though they are saddle point solutions. We also discuss basic properties of the time-dependent solutions.