The Family Group in Grand Unified Theories

TL;DR

This paper reviews symmetry breaking in grand unified theories, discusses models based on $SU_5$, $SO_{10}$, and $E_6$, and presents an $SU_5$ model with a gauged family group, proposing a unification into $SU_8$.

Contribution

It introduces an $SU_5$ model with a gauged family group and sketches a unification approach into $SU_8$, offering new insights into family symmetry breaking.

Findings

The e-family remains massless at the classical level.

Mass corrections to the e-family are calculable.

A potential unification of family and gauge groups into $SU_8$ is proposed.

Abstract

We review the known ways of incorporating and breaking symmetries in a renormalizable way. We summarize the various grand unified theories based on $SU_5, SO_{10}$, and $E_6$ as family enlargement groups. An $SU_5$ model with an $SU_2$ gauged family group is presented as an illustration. In it, the e-family (i.e., e,u and d) is classically massless and acquires calculable mass corrections. The family group is broken by the same agent that does the superstrong breaking. Finally, we sketch a way of unifying the family group with $SU_5$ into $SU_8$.