A combinatorial calculation of the Landau-Ginzburg model $M={\mathbb{C}}^3,W=z_1{z}_2{z}_3$

Abstract

The aim of this paper is to apply ideas from the study of Legendrian singularities to a specific example of interest within mirror symmetry. We calculate the Landau-Ginzburg $A$-model with $M={\mathbb{C}}^3,W=z_1{z}_2{z}_3$ in its guise as microlocal sheaves along the natural singular Lagrangian thimble $L=Cone(T^2)\subset M$. The description we obtain is immediately equivalent to the $B$-model of the pair-of-pants ${\mathbb{P}}^1\setminus \{0,1,\infty \}$ as predicted by mirror symmetry.

11 pages, 1 figure

References in corpus (1)

• Non-characteristic expansions of Legendrian singularities

Cited by in corpus (4)

• Wrapped microlocal sheaves on pairs of pants
• Non-characteristic expansions of Legendrian singularities
• Topological Fukaya category and mirror symmetry for punctured surfaces
• Wall-crossing for toric mutations