Gauged Gromov-Witten theory for small spheres

We relate the genus zero gauged Gromov-Witten invariants of a smooth projective variety for sufficiently small area with equivariant Gromov-Witten invariants. As an application we deduce a gauged version of abelianization for Gromov-Witten invariants in the small area chamber. In the symplectic setting, we prove that any sequence of genus zero symplectic vortices with vanishing area has a subsequence that converges after gauge transformation to a holomorphic map with zero average moment map.