nLab heterotic line bundle

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

• Lara Anderson, James Gray, Andre Lukas, Eran Palti, Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds, Phys. Rev. D 84, 106005 (2011) (arXiv:1106.4804)

• Lara Anderson, James Gray, Andre Lukas, Eran Palti, Heterotic Line Bundle Standard Models, JHEP 2012 113 (2012) 06 [arXiv:1202.1757, doi:10.1007/JHEP06(2012)113]

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

• Lara Anderson, Andrei Constantin, James Gray, Andre Lukas, Eran Palti, A Comprehensive Scan for Heterotic $SU(5)$ GUT models, JHEP01(2014)047 (arXiv:1307.4787)

• Lara Anderson, James Gray, Andre Lukas, Eran Palti, Heterotic standard model database (web)

• Yang-Hui He, Seung-Joo Lee, Andre Lukas, Chuang Sun, Heterotic Model Building: 16 Special Manifolds, J. High Energ. Phys. 2014, 77 (2014) (arXiv:1309.0223)

• Stefan Groot Nibbelink, Orestis Loukas, Fabian Ruehle, Patrick K.S. Vaudrevange, Infinite number of MSSMs from heterotic line bundles?, Phys. Rev. D 92, 046002 (2015) (arXiv:1506.00879)

• Andreas Braun, Callum R. Brodie, Andre Lukas, Heterotic Line Bundle Models on Elliptically Fibered Calabi-Yau Three-folds, JHEP04 (2018) 087 (arXiv:1706.07688)

• James Gray, Juntao Wang, Jumping Spectra and Vanishing Couplings in Heterotic Line Bundle Standard Models, JHEP11 (2019) 073 (arXiv:1906.09373)

• Magdalena Larfors, Robin Schneider, Explore and Exploit with Heterotic Line Bundle Models, Fortschritte der Physik Vol 86 Nr. 5 (arXiv:2003.04817)

Review:

• Andrei Constantin, Heterotic line bundle models, talk at New Developments in Gravity, Cosmology and Strings 2013, Munich 2013 (pdf, pdf)

• Andre Lukas, Line Bundles in String Model Building, talk at StringPhenomenology 2019 (indico:782251/contributions/3441850, pdf, pdf)

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

• Anthony Ashmore, Sebastian Dumitru, Burt Ovrut, Section 4.2 of: Line Bundle Hidden Sectors for Strongly Coupled Heterotic Standard Models, Fortsch. Phys. 69 7 (2021) 2100052 [arXiv:2003.05455, doi:10.1002/prop.202100052]

• Anthony Ashmore, Sebastian Dumitru, Burt Ovrut, Section 2.2 of: Explicit Soft Supersymmetry Breaking in the Heterotic M-Theory B−L MSSM, J. High Energ. Phys. 2021, 33 (2021). (arXiv:2012.11029, doi:10.1007/JHEP08(2021)033)

• Anthony Ashmore, Sebastian Dumitru, Burt Ovrut, Hidden Sectors from Multiple Line Bundles for the B−L MSSM (arXiv:2106.09087)

• Sebastian Dumitru, Burt A. Ovrut, Heterotic M-Theory Hidden Sectors with an Anomalous $U(1)$ Gauge Symmetry (arXiv:2109.13781)

• Sebastian Dumitru, Sec. 2.4 of: The strongly coupled $E_8 \times E_8$ heterotic string: Geometry & Phenomenology [arXiv:2206.12310]

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

• Andreas Braun, Callum Brodie, Andre Lukas, Fabian Ruehle, NS5-Branes and Line Bundles in Heterotic/F-Theory Duality, Phys. Rev. D 98, 126004 (2018) (arXiv:1803.06190, doi:10.1103/PhysRevD.98.126004)

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, $SO(32)$ 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:

• Anthony Ashmore, Rehan Deen, Yang-Hui He, Burt Ovrut, Machine Learning Line Bundle Connections (arXiv:2110.12483)

Appearance of heterotic line bundles via Hypothesis H:

• Domenico Fiorenza, Hisham Sati, Urs Schreiber: Twistorial Cohomotopy implies Green-Schwarz anomaly cancellation, Reviews in Mathematical Physics 34 05 (2022) 2250013 [arXiv:2008.08544, doi:10.1142/S0129055X22500131]

(see commentary on p. 5).