Three-Family SU(5) Grand Unification in String Theory

TL;DR

This paper constructs two novel three-family SU(5) grand unified models within heterotic string theory, featuring distinct hidden sectors and matter contents, advancing string-based GUT model building.

Contribution

It introduces two explicit 3-family SU(5) GUT models in heterotic string theory with unique hidden sectors and matter configurations, expanding the landscape of string-derived GUT models.

Findings

One model has 3 chiral families and 9 Higgs pairs with an SU(2) x SU(2) hidden sector.

The other model features 6 left-handed and 3 right-handed 10s, with an SU(3) hidden sector.

Both models exhibit an anomalous U(1) and specific gauge coupling relations at the string scale.

Abstract

We present two 3-family SU(5) grand unified models in the heterotic string theory. One model has 3 chiral families and 9 pairs of $5+{\overline 5}$ Higgs fields, and an asymptotically-free SU(2) X SU(2) hidden sector, where the two SU(2)s have different matter contents. The other model has 6 left-handed and 3 right-handed 10s, 12 left-handed and 9 right-handed ${\overline 5}$s, and an asymptotically-free SU(3) hidden sector. At the string scale, the gauge couplings $g^2$ of the hidden sector are three times as big as that of SU(5). In addition, both models have an anomalous U(1).