# Boundaries and supercurrent multiplets in 3D Landau-Ginzburg models

## TL;DR

This paper develops a framework for understanding boundaries and supercurrent multiplets in 3D Landau-Ginzburg models with supersymmetry, exploring boundary degrees of freedom and cohomology implications.

## Contribution

It introduces generalized supercurrent multiplets for 3D theories with boundaries, linking bulk and boundary supersymmetry structures, and applies this to Landau-Ginzburg models with matrix factorizations.

## Key findings

- Boundary supercurrent multiplets are explicitly constructed.
- The framework clarifies the role of boundary degrees of freedom.
- Quantization verifies the theoretical predictions.

## Abstract

Theories with 3D $\mathcal{N}=2$ bulk supersymmetry may preserve a 2D $\mathcal{N}=(0,2)$ subalgebra when a boundary is introduced, possibly with localized degrees of freedom. We propose generalized supercurrent multiplets with bulk and boundary parts adapted to such setups. Using their structure, we comment on implications for the $\overline{Q}_+$-cohomology. As an example, we apply the developed framework to Landau-Ginzburg models. In these models, we study the role of boundary degrees of freedom and matrix factorizations. We verify our results using quantization.