# 3D TQFT and HOMFLYPT homology

## TL;DR

This paper introduces a family of 3D topological B-models with target spaces as Hilbert schemes of points in c^2, linking braid interfaces to HOMFLY-PT homology of links.

## Contribution

It establishes a novel connection between 3D topological field theories and HOMFLY-PT homology via Hilbert schemes and braid interfaces.

## Key findings

- Hilbert schemes of points serve as target spaces for 3D B-models.
- Interfaces between theories correspond to braid strands.
- The Hilbert space of a closed braid equals the HOMFLY-PT homology of the link.

## Abstract

We describe a family of 3d topological B-models whose target spaces are Hilbert schemes of points in $\mathbb{C}^2$. The interfaces separating theories with different numbers of points correspond to braid strands. The Hilbert space of the picture of a closed braid is the HOMFLY-PT homology of the corresponding link.