J-kink domain walls and the DBI action

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.

Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and ${mathbb C}P^{N-1}$ Lumps

Topologically stable non-Abelian sine-Gordon solitons have been found recently in the $U(N)$ chiral Lagrangian and a $U(N)$ gauge theory with two $N$ by $N$ complex scalar fields coupled to each other. We construct the effective theory on a non-Abelian sine-Gordon soliton that is a nonlinear sigma model with the target space ${mathbb R} times {mathbb C}P^{N-1}$. We then show that ${mathbb C}P^{N-1}$ lumps on it represent $SU(N)$ Skyrmions in the bulk point of view, providing a physical realization of the rational map Ansatz for Skyrmions of the translational (Donaldson) type. We find therefore that Skyrmions can exist stably without the Skyrme term.

Dyonic non-Abelian vortex strings in supersymmetric and non-supersymmetric theories: tensions and higher derivative corrections

Dyonic non-Abelian local/semi-global vortex strings are studied in detail in supersymmetric/non-supersymmetric Yang-Mills-Higgs theories. While the BPS tension formula is known to be the same as that for the BPS dyonic instanton, we find that the non-BPS tension formula is approximated very well by the well-known tension formula of the BPS dyon. We show that this mysterious tension formula for the dyonic non-BPS vortex stings can be understood from the perspective of a low energy effective field theory. Furthermore, we propose an efficient method to obtain an effective theory of a single vortex string, which includes not only lower derivative terms but also all order derivative corrections by making use of the tension formula. We also find a novel dyonic vortex string whose internal orientation vectors rotate in time and spiral along the string axis.