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

TL;DR

This paper explores supergravity solutions for D3-branes on spaces with R x S^2 x S^3 topology, revealing insights into their geometric structure and implications for gauge theory confinement.

Contribution

It introduces new regular and fractional D3-brane solutions on generalized conifold geometries with a Z_2 symmetry, extending previous models and analyzing their singularity structure.

Findings

Solutions exhibit a horizon coinciding with a curvature singularity.

Presence of fractional branes leads to naked singularities similar to earlier models.

Wilson loop analysis indicates the dual gauge theories are confining.

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.