J-kink domain walls and the DBI action

TL;DR

This paper investigates rotating $J$-kink domain walls in a 4D sigma model, revealing their duality to membranes with constant electromagnetic fields via the DBI action, and classifying their types based on a conserved current.

Contribution

It establishes a duality between $J$-kink domain walls and membranes with electromagnetic fields using the DBI action, and classifies the domain walls into magnetic, null, and electric types.

Findings

$J$-kink domain walls are classified into three types based on $J^2$.

A duality between domain walls and membranes with constant fields is demonstrated.

The effective action of the domain wall coincides with the DBI action for a membrane.

Abstract

We study $J$-kink domain walls in $D=4$ massive $\mathbb{C}P^1$ sigma model. The domain walls are not static but stationary, since they rotate in an internal $S^1$ space with a frequency $\omega$ and a momentum ${\bf k}$ along the domain wall. They are characterized by a conserved current $J_\mu = (Q,{\bf J})$, and are classified into magnetic ($J^2 < 0$), null ($J^2=0$), and electric ($J^2 > 0$) types. Under a natural assumption that a low energy effective action of the domain wall is dual to the $D=4$ DBI action for a membrane, we are lead to a coincidence between the $J$-kink domain wall and the membrane with constant magnetic field $B$ and electric field ${\bf E}$. We also find that $(Q, {\bf J}, \omega, {\bf k})$ is dual to $(B, {\bf E}, H, {\bf D})$ with $H$ and ${\bf D}$ being a magnetizing field and a displacement field, respectively.