D-branes on Nonabelian Threefold Quotient Singularities

TL;DR

This paper studies the moduli space of D-branes on nonabelian Calabi-Yau threefold singularities, revealing topology-changing transitions and introducing a formalism using quivers and algebraic geometry to analyze the Kahler cone.

Contribution

It develops a general formalism for worldvolume theories of D-branes on nonabelian singularities and provides methods to compute the Kahler cone, including toric techniques.

Findings

Topology-changing transitions in the moduli space are characterized.

A procedure for computing the enlarged Kahler cone is established.

Explicit analysis of two low-rank examples demonstrates the methods.

Abstract

We investigate the classical moduli space of D-branes on a nonabelian Calabi-Yau threefold singularity and find that it admits topology-changing transitions. We construct a general formalism of worldvolume field theories in the language of quivers and give a procedure for computing the enlarged Kahler cone of the moduli space. The topology changing transitions achieved by varying the Fayet-Iliopoulos parameters correspond to changes of linearization of a geometric invariant theory quotient and can be studied by methods of algebraic geometry. Quite surprisingly, the structure of the enlarged Kahler cone can be computed by toric methods. By using this approach, we give a detailed discussion of two low-rank examples.