# BPS states, torus links and wild character varieties

## TL;DR

This paper develops a string theoretic approach connecting wild character varieties, refined stable pair theory, and torus link invariants, providing conjectural formulas and generalizations for cases with a unique irregular point.

## Contribution

It introduces a novel string theoretic framework linking wild character varieties to knot invariants and stable pair theory, with explicit conjectural formulas for specific cases.

## Key findings

- Conjectural formulas for wild character varieties with a single irregular point
- A string theoretic construction leading to a colored generalization of known results
- Connections established between wild character varieties, stable pairs, and torus links

## Abstract

A string theoretic framework is constructed relating the cohomology of wild character varieties to refined stable pair theory and torus link invariants. Explicit conjectural formulas are derived for wild character varieties with a unique irregular point on the projective line. For this case the string theoretic construction leads to a conjectural colored generalization of existing results of Hausel, Mereb and Wong as well as Shende, Treumann and Zaslow.