Multi-Flux Warped Throats and Cascading Gauge Theories

TL;DR

The paper investigates how infrared strong coupling in quiver gauge theories for D3-branes at complex cones over del Pezzo surfaces resolves naked IR singularities through quantum deformations of the moduli space, corresponding to geometric complex deformations of the initial singularity. It develops a unified gauge-theory framework, supported by toric/web diagrams, to identify when deformations exist and to construct explicit duality cascades with multiple scales. The results show that many dP_n setups deform to smooth geometries (e.g., conifold-like or fully smooth spaces) and that the gravity duals exhibit multi-region warped throats, while some geometries (notably certain Y^{p,q}) do not admit deformations, yielding persistent IR singularities. The work provides a robust link between IR gauge dynamics and geometric transitions, with implications for flux compactifications, holography beyond KS, and model-building applications.

Abstract

We describe duality cascades and their infrared behavior for systems of D3-branes at singularities given by complex cones over del Pezzo surfaces (and related examples), in the presence of fractional branes. From the gauge field theory viewpoint, we show that D3-branes probing the infrared theory have a quantum deformed moduli space, given by a complex deformation of the initial geometry to a simpler one. This implies that for the dual supergravity viewpoint, the gauge theory strong infrared dynamics smoothes out the naked singularities of the recently constructed warped throat solutions with 3-form fluxes, describing the cascading RG flow of the gauge theory. This behavior thus generalizes the Klebanov-Strassler deformation of the conifold. We describe several explicit examples, including models with several scales of strong gauge dynamics. In the regime of widely separated scales, the dual supergravity solutions should correspond to throats with several radial regions with different exponential warp factors. These rich throat geometries are expected to have interesting applications in compactification and model building. Along our studies, we also construct explicit duality cascades for gauge theories with irrational R-charges, obtained from D-branes probing complex cones over dP1 and dP2.

Figures (32)

• Figure 1: Conifold extremal transition. The finite segment in the first figure represents an $S^2$, with an area proportional to the length of the segment, while the green segment in the last figure corresponds to an $S^3$ with a volume proportional to the distance between the two infinite lines.
• Figure 2: Web diagrams for the complex cones over $dP_0$ and $dP_1$. In both cases, it is impossible to split them into more than one sub-webs in equilibrium, implying there exist no complex deformations for these geometries.
• Figure 3: The web diagram for the complex cone over $dP_2$ and its complex deformation.
• Figure 4: Web diagram for the complex cone over $dP_3$ and its two branches of complex deformation. Figure b) shows a two-dimensional deformation branch, parametrized by the sizes of two independent 3-spheres corresponding to the dashed segments (the three segments are related by a homology relation, hence only two are independent). Figure c) shows a one-dimensional deformation branch.
• Figure 5: Web diagram for a cone over a non-generic blow-up of ${\rm I P}^2$ at four points and its deformation. This geometry is toric and is closely related to $dP_4$. The two dashed segments correspond to two homologically equivalent 3-spheres. The left-over diagram describes a suspended pinch point singularity, which admits a further deformation not shown in the picture.