# A quantized Riemann-Hilbert problem in Donaldson-Thomas theory

## TL;DR

This paper introduces a new class of Riemann-Hilbert problems linked to refined Donaldson-Thomas theory, providing explicit solutions using advanced special functions, and explores their mathematical structure and implications.

## Contribution

It formulates a novel Riemann-Hilbert problem based on refined Donaldson-Thomas theory and constructs explicit solutions using the Barnes double gamma function.

## Key findings

- Defined a new Riemann-Hilbert problem in Donaldson-Thomas theory
- Constructed explicit solutions using Barnes double gamma function
- Analyzed the simplest case in detail

## Abstract

We introduce Riemann-Hilbert problems determined by refined Donaldson-Thomas theory. They involve piecewise holomorphic maps from the complex plane to the group of automorphisms of a quantum torus algebra. We study the simplest case in detail and use the Barnes double gamma function to construct a solution.