Moduli Spaces for D-branes at the Tip of a Cone

TL;DR

This paper links the geometry of Calabi-Yau cones and Fano surfaces to quiver gauge theories and their moduli spaces, revealing how the cone structure appears as a component in the moduli space of certain quiver representations.

Contribution

It constructs a quiver from a Fano surface's derived category and proves its moduli space contains a component isomorphic to the cone over the surface, bridging physics and mathematics.

Findings

The quiver gauge theory's moduli space includes the original cone as a component.

The derived category data leads to a quiver whose representation space reflects the cone geometry.

The approach unifies geometric and algebraic descriptions of D-branes at the cone tip.

Abstract

For physicists: We show that the quiver gauge theory derived from a Calabi-Yau cone via an exceptional collection of line bundles on the base has the original cone as a component of its classical moduli space. For mathematicians: We use data from the derived category of sheaves on a Fano surface to construct a quiver, and show that its moduli space of representations has a component which is isomorphic to the anticanonical cone over the surface.