Uplifting the Iwasawa

Abstract

The Iwasawa manifold is uplifted to seven‐folds of either G2 holonomy or SU(3) structure, explicit new metrics for the same having been constructed in this work. We uplift the Iwasawa manifold to a G2 manifold through “size” deformation (of the Iwasawa metric), via Hitchin’s flow equations. Using results of [1], we also uplift the Iwasawa manifold to a seven‐fold with SU(3) structure through “size” and “shape” deformations via generalisation of Hitchin’s flow equations. For seven‐folds with SU(3)‐structure, the result could be interpreted as M5‐branes wrapping two‐cycles embedded in the seven‐fold (as in [1]) — a warped product of either a special hermitian six‐fold or a balanced six‐fold with an interval.