nLab heterotic line bundle



String theory





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:

  • Evgeny Buchbinder, Andrei Constantin, Andre Lukas, The Moduli Space of Heterotic Line Bundle Models: a Case Study for the Tetra-Quadric, JHEP03 (2014) 025 (arXiv:1311.1941)

  • Magdalena Larfors, Davide Passaro, Robin Schneider, Heterotic Line Bundle Models on Generalized Complete Intersection Calabi Yau Manifolds (arXiv:2010.09763)

  • Steve Abel, Andrei Constantin, Thomas R. Harvey, Andre Lukas, Luca A. Nutricati, Decoding Nature with Nature’s Tools: Heterotic Line Bundle Models of Particle Physics with Genetic Algorithms and Quantum Annealing [arXiv:2306.03147]

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 April 24, 2024 at 17:00:05. See the history of this page for a list of all contributions to it.