Gauge-Higgs models from nilmanifolds

We consider the compactification of a Yang-Mills theory on three-dimensional nilmanifold. The generates in four space-time dimensions, coupled to specific scalar sector. geometry gives rise masses for zero-modes, proportional twist parameter study simple example an SU(3) model broken by non-trivial vacuum potential which three mass scales, two being at tree level, and third one loop level. point out relevance general twisted geometries building particular gauge-Higgs type models, as tree-level hierarchies useful grand unification Higgs sector electroweak symmetry breaking.