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$T$-equivariant disc potential and SYZ mirror construction (1906.11749v4)
Published 27 Jun 2019 in math.SG and math.AG
Abstract: We develop a $G$-equivariant Lagrangian Floer theory and obtain a curved $A_\infty$ algebra, and in particular a $G$-equivariant disc potential. We construct a Morse model, which counts pearly trees in the Borel construction $L_G$. When applied to a smooth moment map fiber of a semi-Fano toric manifold, our construction recovers the $T$-equivariant toric Landau-Ginzburg mirror of Givental. We also study the $\bS1$-equivariant Floer theory of a typical singular SYZ fiber (i.e. a pinched torus) and compute its $\bS1$-equivariant disc potential via the gluing technique developed in \cite{CHL18,HKL}.