Reconstruction of SU(5) Grand Unified Model In Noncommutative Geometry Approach

TL;DR

This paper reconstructs a realistic SU(5) Grand Unified Model within a noncommutative geometry framework, incorporating group actions and a novel curvature term to address symmetry breaking and mass relations.

Contribution

It introduces a new SU(5) GUT model using noncommutative geometry with specific fermion assignments and a linear curvature term for symmetry breaking.

Findings

A new mass relation is derived.

The model successfully incorporates charge conjugation and generation translation.

A linear curvature term is essential for symmetry breaking.

Abstract

Based on the generalized gauge theory on $M^4\times Z_2\times Z_3$, we reconstructed the realistic SU(5) Grand Unified model by a suitable assignment of fermion fields. The action of group elements $Z_2$ on fermion fields is the charge conjugation while the action of $Z_3$ elements represent generation translation. We find that to fit the spontaneous symmetry breaking and gauge hierarchy of SU(5) model a linear term of curvature has to be introduced. A new mass relation is obtained in our reconstructed model.