Gauged Floer theory of toric moment fibers

We investigate the small area limit of the gauged Lagrangian Floer cohomology of Frauenfelder. The resulting cohomology theory, which we call quasimap Floer cohomology, is an obstruction to displaceability of Lagrangians in the symplectic quotient. We use the theory to reproduce the results of Fukaya-Oh-Ohta-Ono and Cho-Oh on non-displaceability of moment fibers of not-necessarily-Fano toric varieties and extend their results to toric orbifolds, without virtual fundamental chains. Finally we describe a conjectural relationship to Floer cohomology in the quotient.