Mirror symmetry for the Landau-Ginzburg A-model $M=\mathbb C^n, W=z_1 \cdots z_n$

TL;DR

This paper computes the category of branes in a specific Landau-Ginzburg A-model using microlocal sheaves and perverse schobers, providing evidence for mirror symmetry in this setting.

Contribution

It introduces a microlocal sheaf approach to the Landau-Ginzburg A-model with a new application of perverse schobers, confirming mirror symmetry predictions.

Findings

Category of branes explicitly calculated

Microlocal sheaves used to model the branes

Results align with mirror symmetry expectations

Abstract

We calculate the category of branes in the Landau-Ginzburg A-model with background $M=\mathbb C^n$ and superpotential $W=z_1 \cdots z_n$ in the form of microlocal sheaves along a natural Lagrangian skeleton. Our arguments employ the framework of perverse schobers, and our results confirm expectations from mirror symmetry.