Branes at Orbifolded Conifold Singularities and Supersymmetric Gauge Field Theories

TL;DR

This work analyzes D3 branes at orbifolded conifold singularities $C_{kl}$ using toric geometry and gauged linear sigma models to map the D-brane Higgs moduli space to (partially) resolved geometries. It shows that distinct geometric phases are connected by flop transitions and that orbifold singularities can emerge as a phase when chiral fields acquire vevs, establishing a link between gauge theory vacua and toric resolutions. The authors provide explicit treatments of ${C}_{22}$ and ${C}_{23}$ (and related ${C}_{32}$) to derive the toric data and quiver gauge theories, and they interpret phase structure in terms of brane-box configurations via T-duality. Partial resolutions are connected to FI parameter choices, and the work clarifies how brane configurations correspond to branes at singularities in these orbifolded conifolds, enriching the understanding of IR phases in string/gauge dualities.$

Abstract

We consider D3 branes at orbifolded conifold singularities which are not quotient singularities. We use toric geometry and gauged linear sigma model to study the moduli space of the gauge theories on the D3 branes. We find that topologically distinct phases are related by a flop transition. It is also shown that an orbifold singularity can occur in some phases if we give expectation values to some of the chiral fields.

Figures (10)

• Figure 1: A toric diagram for ${\bf Z}_5\times {\bf Z}_7$ hyper-quotient of the conifold, ${\cal C}_{57}$
• Figure 2: The $10 \times24$ matrix $T$
• Figure 3: The $14\times 24$ charge matrix $Q$
• Figure 4: The $10\times 24$ matrix $U$
• Figure 5: The $7\times 10$ matrix $V$