Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants

Understand

In this paper we identify the problem of equivariant vortex counting in a $(2,2)$ supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov-Witten invariants of the GIT quotient target space determined by the quiver.

• We provide new contour integral formulae for the ${\cal I}$ and ${\cal J}$-functions encoding the equivariant quantum cohomology of the target space.
• Its chamber structure is shown to be encoded in the analytical properties of the integrand.
• This is explained both via general arguments and by checking several key cases.