Simple Orbifolds Research Articles

Mass deformations of unoriented quiver theories

We study the interplay between mass deformations and unoriented projections of super-conformal quiver gauge theories resulting from D3-branes at (toric) Calabi-Yau singularities. We focus on simple orbifold cases (ℂ3/ℤ3 and ℂ3/ℤ4) and their non-orbifold descendants. This allows us to generalize the construction rules and clarify points that have been previously overlooked. In particular we spell out the conditions of anomaly cancellations as well as super-conformal invariance that typically require the introduction of flavour branes, which in turn may spoil toric symmetry. Finally, we discuss duality cascades in this context and the interplay between Seiberg/toric duality and unoriented projection with (or without) mass deformations.

D terms from D-branes, gauge invariance and moduli stabilization in flux compactifications

We elucidate the structure of D terms in N=1 orientifold compactifications with fluxes. As a case study, we consider a simple orbifold of the type-IIA theory with D6-branes at angles, O6-planes and general NSNS, RR and Scherk-Schwarz geometrical fluxes. We examine in detail the emergence of D terms, in their standard supergravity form, from an appropriate limit of the D-brane action. We derive the consistency conditions on gauged symmetries and general fluxes coming from brane-localized Bianchi identities, and their relation with the Freed-Witten anomaly. We extend our results to other N=1 compactifications and to non-geometrical fluxes. Finally, we discuss the possible role of U(1) D terms in the stabilization of the untwisted moduli from the closed string sector.

Braid pictures for Artin groups

We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical Coxeter diagrams A n , B n = C n and D n and the affine diagrams A n , B n , C n and D n as subgroups of the braid groups of various simple orbifolds. The cases D n , B n , C n and D n are new. In each case the Artin group is a normal subgroup with abelian quotient; in all cases except A n the quotient is finite. We also illustrate the value of our braid calculus by giving a picture-proof of the basic properties of the Garside element of an Artin group of type D n .

Phases of supersymmetric D-branes on Kähler manifolds and the McKay correspondence

We study the topological zero mode sector of type II strings on a K\"ahler manifold $X$ in the presence of boundaries. We construct two finite bases, in a sense bosonic and fermionic, that generate the topological sector of the Hilbert space with boundaries. The fermionic basis localizes on compact submanifolds in $X$. A variation of the FI terms interpolates between the description of these ground states in terms of the ring of chiral fields at the boundary at small volume and helices of exceptional sheaves at large volume, respectively. The identification of the bosonic/fermionic basis with the dual bases for the non-compact/compact K-theory group on $X$ gives a natural explanation of the McKay correspondence in terms of a linear sigma model and suggests a simple generalization of McKay to singular resolutions. The construction provides also a very effective way to describe D-brane states on generic, compact Calabi--Yau manifolds and allows to recover detailed information on the moduli space, such as monodromies and analytic continuation matrices, from the group theoretical data of a simple orbifold.