  A new two dimensional $\mathcal{N}=(0,2)$ Supersymmetric Non-Linear Sigma
Model describes the dynamics of internal moduli of the BPS semi-local vortex
string supported in four dimensional $\mathcal{N}=2$ SQED. While the core of
these strings is very similar to Abrikosov-Nielsen-Olesen vortices, they are
defined with a characteristic size modulus, much like the instanton lump size.
This entails that the constituting fields of the vortex do not decay
exponentially, as one goes far away from the core of the string, but as a
rational function. The appearance of an extra scale in the problem also allows
for an explicit, analytic, approximate solution to be written for the BPS
equation, surprisingly.
  Despite the conceptually large differences between semi-local and non-Abelian
vortices, it appears that the moduli structures have one main common feature,
both undergo the same kind of heterotic deformation when a supersymmetry
breaking potential term is added to the spacetime theory, moving from
$\mathcal{N}=2$ to $\mathcal{N}=1$.
  By adding a mass term for the gauge scalar multiplet, a heterotic deformation
develops on the worldsheet, which breaks supersymmetry down to $(0,2)$ by
coupling supertranslational fermionic zero modes to supersize ones. Such an
interaction between zero modes of two different sectors was already
hypothesized and subsequently found for non-Abelian strings, providing a neat
way of circumventing accidental supersymmetry enhancement via Zumino's theorem.
We find that, for small values of the spacetime mass term, an entirely
analogous term develops on the worldsheet of semi-local strings.
