D-branes on Nonabelian Threefold Quotient Singularities

In a geometrical background, D-brane charge is classified by topological K-theory. The corresponding classification of D-brane charge in an arbitrary, nongeometrical, compactification is still a mystery. We study D-branes on non-simply-connected Calabi-Yau 3-folds, with particular interest in the D-branes whose charges are torsion elements of the K-theory. We argue that we can follow the D-brane charge through the nongeometrical regions of the Kahler moduli space and, as evid...

A class of noncommutative spaces, named `soft noncommutative schemes via toric geometry', are constructed and the mathematical model for (dynamical/nonsolitonic, complex algebraic) D-branes on such a noncommutative space, following arXiv:0709.1515 [math.AG] (D(1)), is given. Any algebraic Calabi-Yau space that arises from a complete intersection in a smooth toric variety can embed as a commutative closed subscheme of some soft noncommutative scheme. Along the study, the notio...

We initiate a systematic study of 2d (0,2) quiver gauge theories on the worldvolume of D1-branes probing singular toric Calabi-Yau 4-folds. We present an algorithm for efficiently calculating the classical mesonic moduli spaces of these theories, which correspond to the probed geometries. We also introduce a systematic procedure for constructing the gauge theories for arbitrary toric singularities by means of partial resolution, which translates to higgsing in the field theor...

In this paper we present simplifying techniques which allow one to compute the quiver diagrams for various D-branes at (non-Abelian) orbifold singularities with and without discrete torsion. The main idea behind the construction is to take the orbifold of an orbifold. Many interesting discrete groups fit into an exact sequence $N\to G\to G/N$. As such, the orbifold $M/G$ is easier to compute as $(M/N)/(G/N)$ and we present graphical rules which allow fast computation given th...

In this note we study the resolution of conifold singularity by D-branes by considering compactification of D-branes on $\C^3/(\Z_2\times\Z_2)$. The resulting vacuum moduli space of D-branes is a toric variety which turns out to be a resolved conifold, that is a nodal variety in $\C^4$. This has the implication that all the corresponding phases of Type--II string theory are geometrical and are accessible to the D-branes, since they are related by flops.

We study topological properties of the D-brane resolution of three-dimensional orbifold singularities, C^3/Gamma, for finite abelian groups Gamma. The D-brane vacuum moduli space is shown to fill out the background spacetime with Fayet--Iliopoulos parameters controlling the size of the blow-ups. This D-brane vacuum moduli space can be classically described by a gauged linear sigma model, which is shown to be non-generic in a manner that projects out non-geometric regions in i...

We discuss examples of D-branes probing toric singularities, and the computation of their world-volume gauge theories from the geometric data of the singularities. We consider several such examples of D-branes on partial resolutions of the orbifolds ${\bf C^3/Z_2\times Z_2}$,${\bf C^3/Z_2\times Z_3}$ and ${\bf C^4/Z_2\times Z_2 \times Z_2}$.

We give an overview of recent work on Dirichlet branes on Calabi-Yau threefolds which makes contact with Kontsevich's homological mirror symmetry proposal, proposes a new definition of stability which is appropriate in string theory, and provides concrete quiver categories equivalent to certain categories of branes on CY. To appear in the proceedings of the 3rd European Congress of Mathematics.

We study the classification of D-branes in all compact Lie groups including non-simply-laced ones. We also discuss the global structure of the quantum moduli space of the D-branes. D-branes are classified according to their positions in the maximal torus. We describe rank 2 cases, namely $B_2$, $C_2$, $G_2$, explicitly and construct all the D-branes in $B_r$, $C_r$, $F_4$ by the method of iterative deletion in the Dynkin diagram. The discussion of moduli space involves global...

We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) (dP0)^3 singularity, its embedding in a specific Calab...