Gauge-Higgs models from Nilmanifolds

TL;DR

This paper explores how compactifying Yang-Mills theories on nilmanifolds creates mass hierarchies in gauge-Higgs models, with potential applications in grand unification and electroweak symmetry breaking.

Contribution

It demonstrates that nilmanifold compactifications induce specific mass spectra and hierarchies, offering new geometric tools for model building in gauge-Higgs theories.

Findings

Masses for zero-modes are proportional to the nilmanifold's twist parameter.

A specific SU(3) model exhibits three distinct mass scales, two at tree level and one at loop level.

Twisted geometries can generate tree-level mass hierarchies relevant for grand unification and Higgs sectors.

Abstract

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