Branes with fluxes wrapped on spheres

TL;DR

This paper constructs and analyzes supergravity solutions describing D6-branes wrapped on Kahler four-cycles, exploring their geometric interpolations, deformations with fluxes, and connections to AdS/CFT and Freund-Rubin compactifications.

Contribution

It provides the most general supergravity solutions for D6-branes wrapped on product of spheres, including flux deformations and their IR/UV behavior, linking to known compactification models.

Findings

Interpolates between Calabi-Yau four-fold and product of spheres or flat spaces.

Shows deformation of solutions with background four-form fluxes.

Identifies flow from Calabi-Yau times Minkowski space to AdS_4xQ^{1,1,1}.

Abstract

Following an eight-dimensional gauged supergravity approach we construct the most general solution describing D6-branes wrapped on a Kahler four-cycle taken to be the product of two spheres of different radii. Our solution interpolates between a Calabi-Yau four-fold and the spaces S^2xS^2xS^2xR^2 or S^2xS^2xR^4, depending on generic choices for the parameters. Then we turn on a background four-form field strength, corresponding to D2-branes, and show explicitly how our solution is deformed. For a particular choice of parameters it represents a flow from a Calabi-Yau four-fold times the three-dimensional Minkowski space-time in the ultraviolet, to the space-time AdS_4xQ^{1,1,1} in the infrared. In general, the solution in the infrared has a singularity which within type-IIA supergravity corresponds to the near horizon geometry of the solution for the D2-D6 system. Finally, we uncover the relation with work done in the eighties on Freund-Rubin type compactifications.