  The quantum worldsheet dynamics of vortex strings contains information about
the 4d non-Abelian gauge theory in which the string lives. Here I tell this
story. The string worldsheet theory is typically some variant of the CP^{N-1}
sigma-model, describing the orientation of the string in a U(N) gauge group.
Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories
have been known since the 1970s. The vortex string provides a quantitative link
between the two. In 4d theories with N=2 supersymmetry, the exact BPS spectrum
of the worldsheet coincides with the bulk spectrum in 4d. Moreover, by tuning
parameters, the CP^{N-1} sigma-model can be coaxed to flow to an interacting
conformal fixed point which is related to the 4d Argyres-Douglas fixed point.
For theories with N=1 supersymmetry, the worldsheet theory suffers dynamical
supersymmetry breaking and, more interestingly, supersymmetry restoration, in a
way which captures the physics of Seiberg's quantum deformed moduli space.
