Gamma II for toric varieties from integrals on T-dual branes and homological mirror symmetry

Abstract

In this paper we consider the oscillatory integrals on Lefschetz thimbles in the Landau-Ginzburg model as the mirror of a toric Fano manifold. We show these thimbles represent the same relative homology classes as the characteristic cycles of the corresponding constructible sheaves under the equivalence of \cite{GPS18-2}. Then the oscillatory integrals on such thimbles are the same as the integrals on the characteristic cycles and relate to genus $0$ Gromov-Witten descendant potential for $X$, and this leads to a proof of Gamma II conjecture for toric Fano manifolds.

arXiv comment24 pages, 2 figures

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Cited by in corpus (1)

• Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks