3-branes on spaces with R x S^2 x S^3 topology

TL;DR

This work constructs and analyzes D3-brane solutions with six-dimensional transverse spaces of topology $R\times S^2\times S^3$, extended by a one-parameter family $b$ (and in some cases $a$) of Ricci-flat, Kähler metrics on generalized conifolds. The authors show that, for $b\neq 0$, the conifold and resolved conifold geometries can be rendered regular via a ${\bf Z}_2$ quotient, while the deformed conifold develops a horizon coincident with a curvature singularity; when fractional D3-branes are included, repulson-type naked singularities emerge behind the zero-charge locus. Pure D3-brane backgrounds exhibit non-AdS$_5$ near-core behavior (except at $b=0$, which preserves AdS$_5\times T^{1,1}$ in the IR) and display confinement in the Wilson-loop analysis, indicating robust IR dynamics despite the geometric generalizations. The results enhance understanding of how IR scales, supersymmetry, and confinement emerge in gauge/gravity duals with richer transverse geometry, and highlight the role of the $b$ parameter as an infrared mass/confinement scale. The paper also clarifies how fluxes and geometry interact to produce (or obstruct) regular, confining dual gauge theories in these generalized conifold backgrounds.

Abstract

We study supergravity solutions representing D3-branes with transverse 6-space having R x S^2 x S^3 topology. We consider regular and fractional D3-branes on a natural one-parameter extensions of the standard Calabi-Yau metrics on the singular and resolved conifolds. After imposing a Z_2 identification on an angular coordinate these generalized "6-d conifolds" are nonsingular spaces. The backreaction of D3-branes creates a curvature singularity that coincides with a horizon. In the presence of fractional D3-branes the solutions are similar to the original ones in hep-th/0002159, hep-th/0010088: the metric has a naked repulson-type singularity located behind the radius where the 5-form flux vanishes. The semiclassical behavior of the Wilson loop suggests that the corresponding gauge theory duals are confining.