D-particles on T^4/Z_n orbifolds and their resolutions

TL;DR

This paper develops a gauge theory framework for D-particles on $T^4/Z_n$ orbifolds, showing that Fayet-Iliopoulos terms can resolve singularities and potentially produce a $K3$ surface.

Contribution

It formulates the effective field theory of D-particles on orbifolds as a gauge theory on a $V$-bundle and explores singularity resolution via Fayet-Iliopoulos terms.

Findings

Fayet-Iliopoulos terms can resolve orbifold singularities.

Potential realization of $K3$ surfaces through blow-up of fixed points.

Evidence for smooth geometries emerging from singular orbifolds.

Abstract

We formulate the effective field theory of a D-particle on orbifolds of $T^4$ by a cyclic group as a gauge theory in a $V$-bundle over the dual orbifold. We argue that this theory admits Fayet-Iliopoulos terms analogous to those present in the case of noncompact orbifolds. In the $n=2$ case, we present some evidence that turning on such terms resolves the orbifold singularities and may lead to a $K3$ surface realized as a blow up of the fixed points of the cyclic group action.