Self-dual quiver moduli and orientifold Donaldson-Thomas invariants

TL;DR

This paper studies moduli spaces of self-dual quiver representations motivated by string theory, developing Hall module techniques to compute point counts and establish wall-crossing formulas for orientifold BPS invariants.

Contribution

It introduces a novel approach to compute and analyze orientifold Donaldson-Thomas invariants using Hall modules and wall-crossing formulas in the context of self-dual quiver representations.

Findings

Developed Hall module techniques for counting self-dual quiver representations over finite fields.

Derived wall-crossing formulas matching predictions from string theory.

Reformulated wall-crossing in finite type cases using quantum dilogarithm identities.

Abstract

Motivated by the counting of BPS states in string theory with orientifolds, we study moduli spaces of self-dual representations of a quiver with contravariant involution. We develop Hall module techniques to compute the number of points over finite fields of moduli stacks of semistable self-dual representations. Wall-crossing formulas relating these counts for different choices of stability parameters recover the wall-crossing of orientifold BPS/Donaldson-Thomas invariants predicted in the physics literature. In finite type examples the wall-crossing formulas can be reformulated in terms of identities for quantum dilogarithms acting in representations of quantum tori.