Abelian Higgs vortex moduli space
= Abelian Higgs vortex moduli space
{c}
{title2=$\mathcal M_N$}
At critical coupling, the Abelian Higgs vortex moduli space is the space of gauge-equivalence classes of static $N$-vortex solutions. Vortex positions provide complex coordinates, and the field-theory kinetic energy induces an $L^2$ Riemannian metric whose geodesics approximate slow vortex motion.