Branes with fluxes wrapped on spheres

Abstract

Following an eight-dimensional gauged supergravity approach we construct the most general solution describing D6-branes wrapped on a Kähler 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 2 × S2 × S2 × ℝ2 or S2 × S2 × ℝ4, 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 AdS4 × Q1,1,1 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. © SISSA/ISAS 2002.