$T$-equivariant disc potentials for toric Calabi-Yau manifolds

Abstract

We study the equivariant disc potentials for immersed SYZ fibers in toric Calabi-Yau manifolds. The immersed Lagrangians play a crucial role in the partial compactification of the SYZ mirrors. Morever, their equivariant disc potentials have a close relation with that of Aganagic-Vafa branes. We show that the potentials can be computed by using an equivariant version of isomorphisms in the Fukaya category.