nLab heterotic line bundle



String theory




Classes of bundles

Universal bundles






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(U(1) n)SU(n)E 82n5 S\big( U(1)^n \big) \;\subset\; SU(n) \; \subset\; E_8 \;\;\;\;\; 2 \leq n \leq 5

(the direct product group of (n1)(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=4,5n = 4,5 lead to good phenomenology, while for the hidden sector the value n=2n = 2 is used (in ADO 20a, Sec. 4.2, ADO 20a, Sec. 2.2).


Heterotic line bundle models were first considered in

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


On heterotic line bundles in the hidden sector of heterotic M-theory:

On heterotic line bundles seen in F-theory under duality between M/F-theory and heterotic string theory:

See also:

Similar discussion in SemiSpin(32)-heterotic string theory:

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

Discussion via machine learning of connections on heterotic line bundles over Calabi-Yau 3-folds:

Appearance of heterotic line bundles via Hypothesis H:

(see commentary on p. 5).

Last revised on July 23, 2022 at 17:50:21. See the history of this page for a list of all contributions to it.