nLab heterotic string phenomenology -- references

Heterotic string phenomenology

The historical origin of all string phenomenology is the top-down GUT-model building in heterotic string theory due to

• Philip Candelas, Gary Horowitz, Andrew Strominger, Edward Witten, Vacuum configurations for superstrings, Nuclear Physics B Volume 258, 1985, Pages 46-74 Nucl. Phys. B 258, 46 (1985) [doi:10.1016/0550-3213(85)90602-9]

Review and exposition:

• Edward Witten, Quest For Unification, Heinrich Hertz lecture at SUSY 2002 at DESY, Hamburg [arXiv:hep-ph/0207124]

• Hans-Peter Nilles, Strings, Exceptional Groups and Grand Unification, talk at Planck 2011 [pdf, pdf]

• Saul Ramos-Sanchez, Michael Ratz, Heterotic Orbifold Models, in Handbook of Quantum Gravity, Springer (2024) [doi:10.1007/978-981-19-3079-9,

  arXiv:2401.03125]

The $E_8 \times E_8$-heterotic string

The following articles claim the existence of exact realization of the gauge group and matter-content of the MSSM in heterotic string theory on orbifolds (not yet checking Yukawa couplings):

• Volker Braun, Yang-Hui He, Burt Ovrut, Tony Pantev, A Heterotic Standard Model, Phys. Lett. B618 : 252-258 2005 (arXiv:hep-th/0501070)

• Wilfried Buchmuller, Koichi Hamaguchi, Oleg Lebedev, Michael Ratz, Supersymmetric Standard Model from the Heterotic String, Phys. Rev. Lett. 96 121602 (2006) ([doi:varXiv:hep-ph/0511035]

• Volker Braun, Yang-Hui He, Burt Ovrut, Tony Pantev, The Exact MSSM Spectrum from String Theory, JHEP 0605:043, 2006 (arXiv:hep-th/0512177)

• Vincent Bouchard, Ron Donagi, An SU(5) Heterotic Standard Model, Phys. Lett. B633:783-791,2006 (arXiv:hep-th/0512149)

A computer search through the “landscape” of Calabi-Yau varieties showed severeal hundreds more such exact heterotic standard models (about one billionth of all CYs searched, and most of them arising as SU(5)-GUTs):

general computational theory:

• Lara Anderson, Yang-Hui He, Andre Lukas, Heterotic Compactification, An Algorithmic Approach, JHEP 0707:049, 2007 (arXiv:hep-th/0702210)

using heterotic line bundle models:

• 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 JHEP06(2012)113 (arXiv:1202.1757)

• 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)

• 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)

• Andrei Constantin, Yang-Hui He, Andre Lukas, Counting String Theory Standard Models, Physics Letters B

  Volume 792, 10 May 2019, Pages 258-262 (arXiv:1810.00444)

• Alon E. Faraggi, Glyn Harries, Benjamin Percival, John Rizos, Towards machine learning in the classification of $\mathbb{Z}_2 \times \mathbb{Z}_2$ orbifold compactifications (arXiv:1901.04448)

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

The resulting database of heterotic line bundle models is here:

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

Review includes

• Lara Anderson, New aspects of heterotic geometry and phenomenology, talk at Strings2012, Munich 2012 (pdf)

• Yang-Hui He, Deep-learning the landscape, talk at String and M-Theory: The new geometry of the 21st century (pdf slides, video recording)

• Yang-Hui He, Calabi-Yau Spaces in the String Landscape (arXiv:2006.16623)

Computation of metrics on these Calabi-Yau compactifications (eventually needed for computing their induced Yukawa couplings) is started in

• Volker Braun, Tamaz Brelidze, Michael Douglas, Burt Ovrut, Calabi-Yau Metrics for Quotients and Complete Intersections, JHEP 0805:080, 2008 (arXiv:0712.3563)

and via machine learning:

• Andrei Constantin, Cristofero S. Fraser-Taliente, Thomas R. Harvey, Andre Lukas, Burt Ovrut, Computation of Quark Masses from String Theory [arXiv:2402.01615]

This “heterotic standard model” has a “hidden sector” copy of the actual standard model, more details of which are discussed here:

• Volker Braun, Yang-Hui He, Burt Ovrut, Supersymmetric Hidden Sectors for Heterotic Standard Models (arXiv:1301.6767)

The issue of moduli stabilization in these kinds of models is discussed in

• Michele Cicoli, Senarath de Alwis, Alexander Westphal, Heterotic Moduli Stabilization (arXiv:1304.1809)

• Lara Anderson, James Gray, Andre Lukas, Burt Ovrut, Vacuum Varieties, Holomorphic Bundles and Complex Structure Stabilization in Heterotic Theories (arXiv:1304.2704)

Principles singling out heterotic models with three generations of fundamental particles are discussed in:

• Philip Candelas, Xenia de la Ossa, Yang-Hui He, Balazs Szendroi, Triadophilia: A Special Corner in the Landscape, Adv.Theor.Math.Phys.12:2,2008 (arXiv:0706.3134)

Discussion of non-supersymmetric: GUT models:

• Alon E. Faraggi, Viktor G. Matyas, Benjamin Percival, Classification of Non-Supersymmetric Pati-Salam Heterotic String Models (arXiv:2011.04113)

See also:

• Carlo Angelantonj, Ioannis Florakis, GUT Scale Unification in Heterotic Strings (arXiv:1812.06915)

The $SemiSpin(32)$-heterotic string

Discussion of string phenomenology for the SemiSpin(32)-heterotic string (see also at type I phenomenology):

• Kang-Sin Choi, Stefan Groot Nibbelink, Michele Trapletti, Heterotic $SO(32)$ model building in four dimensions, JHEP 0412:063, 2004 (arXiv:hep-th/0410232)

• Hans-Peter Nilles, Saul Ramos-Sanchez, Patrick K.S. Vaudrevange, Akin Wingerter, Exploring the $SO(32)$ Heterotic String, JHEP 0604:050 (2006) [doi:10.1088/1126-6708/2006/04/050arXiv:hep-th/0603086]

• Saul Ramos-Sanchez, Towards Low Energy Physics from the Heterotic String, Fortsch. Phys. 10 (2009) 907-1036 [doi:10.1002/prop.200900073arXiv:0812.3560]

  (heterotic SemiSpin(32) R-parity MSSM vacua)

• Naoki Yamatsu, String-Inspired Special Grand Unification, Progress of Theoretical and Experimental Physics, Volume 2017, Issue 10, 1 (arXiv:1708.02078, doi:10.1093/ptep/ptx135)

• Jihn E. Kim, Grand unfication models from $SO(32)$ heterotic string (arXov:2008.00367)

On heterotic line bundle models:

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

The “$SO(16)\times SO(16)$”-heterotic string

This non-supersymmetric string theory was first described in:

• Luis Alvarez-Gaumé, Paul Ginsparg, Gregory Moore and Cumrun Vafa, An $O(16)\times O(16)$ heterotic string, Phys. Lett. B 171 (1986) 155 [doi:10.1016/0370-2693(86)91524-8]

• Lance Dixon and Jeffrey Harvey, String Theories in Ten-Dimensions Without Space-Time Supersymmetry, Nucl. Phys. B 274 (1986) 93 [doi:10.1016/0550-3213(86)90619-X]

A proposal on what the correct global character of the gauge group is appears in:

• Brett McInnes, The Semispin Groups in String Theory, J. Math. Phys. 40 (1999) 4699-4712 [arXiv:hep-th/9906059, doi:10.1063/1.532999]

A suggestion that the $SO(16)\times SO(16)$ heterotic string is a the $E_8\times E_8$ string “minus” the semispin group $\text{Spin}(32)/\mathbb{Z}_2$:

• Adrian Norbert Schellekens, and Nicholas Warner Anomalies, characters and strings, Nuclear Physics B 287 (1987) 317-361 [doi:10.1016/0550-3213(87)90108-8]