Equivariant Lagrangian Floer theory on compact toric manifolds

We define an equivariant Lagrangian Floer theory on compact symplectic toric manifolds for the subtorus actions. We prove that the set of Lagrangian torus fibers (with weak bounding cochain data) with non-vanishing equivariant Lagrangian Floer cohomology forms a rigid analytic space. We can apply tropical geometry to locate such Lagrangian torus fibers in the moment map. We show that these Lagrangian submanifolds are nondisplaceable by equivariant Hamiltonian diffeomorphisms.