Linking disks, spinning vortices and exponential networks of augmentation curves

TL;DR

This paper introduces a mirror derivation of the quiver description of open topological strings, connecting augmentation curves, exponential networks, and BPS vortices to provide a new perspective on the knots-quivers correspondence.

Contribution

It presents a novel mirror derivation linking augmentation curves and exponential networks to the quiver description of open topological strings, based on enumerative invariants.

Findings

Quivers are derived from M2 branes wrapping holomorphic disks with boundary conditions.

Holomorphic disks are shown to be mirror to calibrated 1-chains on augmentation curves.

Intersections of these chains encode boundary linking information.

Abstract

We propose a mirror derivation of the quiver description of open topological strings known as the knots-quivers correspondence, based on enumerative invariants of augmentation curves encoded by exponential networks. Quivers are obtained by studying M2 branes wrapping holomorphic disks with Lagrangian boundary conditions on an M5 brane, through their identification with a distinguished sector of BPS kinky vortices in the 3d-3d dual QFT. Our proposal suggests that holomorphic disks with Lagrangian boundary conditions are mirror to calibrated 1-chains on the associated augmentation curve, whose intersections encode the linking of boundaries.