T-equivariant disc potential and SYZ mirror construction

Abstract

We develop a G-equivariant Lagrangian Floer theory by counting pearly trees in the Borel construction LG. We apply the construction to smooth moment-map fibers of toric semi-Fano manifolds and obtain the T-equivariant Landau-Ginzburg mirrors. We also apply this to the typical S^1-invariant SYZ singular fiber, which is the single-pinched torus, and compute its S^1-equivariant disc potential.First author draf