D-branes on Fourfolds with Discrete Torsion

TL;DR

This paper investigates the effects of discrete torsion on D1-branes in a specific orbifold, revealing how it modifies the gauge theory and preserves certain singularities in the moduli space.

Contribution

It introduces a method to incorporate discrete torsion via projective representations and analyzes the resulting deformation of the gauge theory's moduli space.

Findings

Discrete torsion is incorporated through projective representations.

The moduli space retains a codimension three singularity.

Deformation of the F-flatness condition affects the gauge theory.

Abstract

We study D1-branes on the fourfold $\C^4/(\Z_2\times\Z_2\times\Z_2)$, in the presence of discrete torsion. Discrete torsion is incorporated in the gauge theory of the D1-branes by considering a projective representation of the finite group $\Z_2\times\Z_2\times\Z_2$. The corresponding orbifold is then deformed by perturbing the F-flatness condition of the gauge theory. The moduli space of the resulting gauge theory retains a stable singularity of codimension three.