Baby Skyrme model, near-BPS approximations, and supersymmetric extensions

We study the baby Skyrme model as a theory that interpolates between two distinct BPS systems. For this, a near-BPS approximation can be used when there is a small deviation from each of the two BPS limits. We provide analytical explanation and numerical support for the validity of this approximation. We then study the set of all possible supersymmetric extensions of the baby Skyrme model with $\mathcal{N}=1$ and the particular ones with extended $\mathcal{N}=2$ supersymmetries and relate this to the above mentioned almost-BPS approximation.

Figure 1

In the first plot, first row, the mass of the soliton normalized to the BPS lower bound $4\pi$ for $k=2$ is plotted as a function of $\zeta$. The upper bounds are the two near-BPS approximations (blown up in the plots below). The second plot, first row, presents the corresponding radial profiles for $f(r)$ for various values of $\zeta$. Thus, it shows the flow between the two almost-BPS solutions as $\zeta$ varies over the interval [0, 1]. The plots in the second row are the mass plot zoomed near the two edges of the interval.

Figure 2

As Fig. 1 but for $k=6$.

Figure 3

As Figs. 1 and 2 but this time for $k=1$.

Figure 4

Supersymmetric extensions of the baby Skyrme model.

Figure 5

A “short” $\mathcal{N}=2$ multiplet is lifted to a “long” $\mathcal{N}=1$ multiplet when supersymmetry is partially broken.