# nLab heterotic line bundle

Contents

## Phenomenology

#### Bundles

bundles

fiber bundles in physics

# Contents

## Idea

If the gauge-complex vector bundle in a heterotic string theory vacuum has reduction of the structure group to an abelian group of the form

$S\big( U(1)^n \big) \;\subset\; SU(n) \; \subset\; E_8 \;\;\;\;\; 2 \leq n \leq 5$

(the direct product group of $(n-1)$-copies of the circle group, regarded as a diagonal subgroup of SU(n) and thus of E8)

it is called a heterotic line bundle in Anderson-Gray-Lukas-Palti 11.

Considering these models has led to a little revolution in heterotic string phenomenology (Anderson-Gray-Lukas-Palti 12).

In the observable sector of heterotic M-theory the values $n = 4,5$ lead to good phenomenology, while for the hidden sector the value $n = 2$ is used (in ADO 20a, Sec. 4.2, ADO 20a, Sec. 2.2).

## References

Heterotic line bundle models were first considered in

The resulting scan of SU(5) GUT vacua among heterotic line bundle models:

Review:

• Hajime Otsuka, $SO(32)$ heterotic line bundle models, JHEP 05 (2018) 045 (arXiv:1801.03684)