A Riemann-Hilbert problem for uncoupled BPS structures

TL;DR

This paper investigates a Riemann-Hilbert problem linked to uncoupled BPS structures, demonstrating the existence of unique solutions expressed through Gamma functions and reconstructing the associated connection.

Contribution

It provides a novel analysis of the Riemann-Hilbert problem for uncoupled BPS structures, establishing the explicit form of solutions and their connection reconstruction.

Findings

Unique meromorphic solutions expressed via Gamma functions

Reconstruction of the associated connection

Clarification of the Riemann-Hilbert problem for uncoupled BPS structures

Abstract

We study the Riemann-Hilbert problem attached to an uncoupled BPS structure proposed by Bridgeland in "Riemann-Hilbert problems from Donaldson-Thomas theory". We show that it has "essentially" unique meromorphic solutions given by a product of Gamma functions. We reconstruct the corresponding connection.