[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Exploring positive monad bundles and a new heterotic standard model

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

A complete analysis of all heterotic Calabi-Yau compactifications based on positive two-term monad bundles over favourable complete intersection Calabi-Yau threefolds is performed. We show that the original data set of about 7000 models contains 91 standard-like models which we describe in detail. A closer analysis of Wilson-line breaking for these models reveals that none of them gives rise to precisely the matter field content of the standard model. We conclude that the entire set of positive two-term monads on complete intersection Calabi-Yau manifolds is ruled out on phenomenological grounds. We also take a first step in analyzing the larger class of non-positive monads. In particular, we construct a supersymmetric heterotic standard model within this class. This model has the standard model gauge group and an additional U(1)B−L symmetry, precisely three families of quarks and leptons, one pair of Higgs doublets and no anti-families or exotics of any kind.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985) 46 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  2. E. Witten, New issues in manifolds of SU(3) holonomy, Nucl. Phys. B 268 (1986) 79 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. M.B. Green, J.H. Schwarz and E. Witten, Superstring theory, volume 2, Cambridge University Press, Cambridge U.K. (1987).

    MATH  Google Scholar 

  4. A. Lukas, B.A. Ovrut, K.S. Stelle and D. Waldram, The universe as a domain wall, Phys. Rev. D 59 (1999) 086001 [hep-th/9803235] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  5. L.B. Anderson, Y.-H. He and A. Lukas, Heterotic compactification, an algorithmic approach, JHEP 07 (2007) 049 [hep-th/0702210] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. L.B. Anderson, Y.-H. He and A. Lukas, Monad bundles in heterotic string compactifications, JHEP 07 (2008) 104 [arXiv:0805.2875] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. L.B. Anderson, Heterotic and M-theory Compactifications for String Phenomenology, arXiv:0808.3621 [SPIRES].

  8. R. Donagi, Y.-H. He, B.A. Ovrut and R. Reinbacher, The particle spectrum of heterotic compactifications, JHEP 12 (2004) 054 [hep-th/0405014] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. Y.-H. He, GUT particle spectrum from heterotic compactification, Mod. Phys. Lett. A 20 (2005) 1483 [SPIRES].

    ADS  Google Scholar 

  10. R. Donagi, Y.-H. He, B.A. Ovrut and R. Reinbacher, Moduli dependent spectra of heterotic compactifications, Phys. Lett. B 598 (2004) 279 [hep-th/0403291] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  11. V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, A heterotic standard model, Phys. Lett. B 618 (2005) 252 [hep-th/0501070] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  12. V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, A standard model from the E 8 × E 8 heterotic superstring, JHEP 06 (2005) 039 [hep-th/0502155] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, The exact MSSM spectrum from string theory, JHEP 05 (2006) 043 [hep-th/0512177] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. V. Bouchard and R. Donagi, An SU(5) heterotic standard model, Phys. Lett. B 633 (2006) 783 [hep-th/0512149] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  15. R. Donagi, Y.-H. He, B.A. Ovrut and R. Reinbacher, Higgs doublets, split multiplets and heterotic SU(3) C × SU(2) L × U(1) Y spectra, Phys. Lett. B 618 (2005) 259 [hep-th/0409291] [SPIRES].

    ADS  Google Scholar 

  16. R. Donagi, Y.-H. He, B.A. Ovrut and R. Reinbacher, The spectra of heterotic standard model vacua, JHEP 06 (2005) 070 [hep-th/0411156] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. R. Blumenhagen, S. Moster and T. Weigand, Heterotic GUT and standard model vacua from simply connected Calabi-Yau manifolds, Nucl. Phys. B 751 (2006) 186 [hep-th/0603015] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. R. Blumenhagen, S. Moster, R. Reinbacher and T. Weigand, Massless spectra of three generation U(N) heterotic string vacua, JHEP 05 (2007) 041 [hep-th/0612039] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. V. Bouchard, M. Cvetič and R. Donagi, Tri-linear couplings in an heterotic minimal supersymmetric standard model, Nucl. Phys. B 745 (2006) 62 [hep-th/0602096] [SPIRES].

    Article  ADS  Google Scholar 

  20. A. Bak, V. Bouchard and R. Donagi, Exploring a new peak in the heterotic landscape, arXiv:0811.1242 [SPIRES].

  21. L.B. Anderson, J. Gray, D. Grayson, Y.-H. He and A. Lukas, Yukawa couplings in heterotic compactification, arXiv:0904.2186 [SPIRES].

  22. Y.-H. He, S.-J. Lee and A. Lukas, Heterotic models from vector bundles on toric Calabi-Yau manifolds, arXiv:0911.0865 [SPIRES].

  23. O. Lebedev, H.P. Nilles, S. Ramos-Sanchez, M. Ratz and P.K.S. Vaudrevange, Heterotic mini-landscape (II): completing the search for MSSM vacua in a Z 6 orbifold, Phys. Lett. B 668 (2008) 331 [arXiv:0807.4384] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  24. O. Lebedev et al., The heterotic road to the MSSM with R parity, Phys. Rev. D 77 (2008) 046013 [arXiv:0708.2691] [SPIRES].

    ADS  Google Scholar 

  25. O. Lebedev et al., Low energy supersymmetry from the heterotic landscape, Phys. Rev. Lett. 98 (2007) 181602 [hep-th/0611203] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  26. O. Lebedev et al., A mini-landscape of exact MSSM spectra in heterotic orbifolds, Phys. Lett. B 645 (2007) 88 [hep-th/0611095] [SPIRES].

    ADS  Google Scholar 

  27. T. Kobayashi, S. Raby and R.-J. Zhang, Constructing 5D orbifold grand unified theories from heterotic strings, Phys. Lett. B 593 (2004) 262 [hep-ph/0403065] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  28. T. Kobayashi, S. Raby and R.-J. Zhang, Searching for realistic 4d string models with a Pati-Salam symmetry: orbifold grand unified theories from heterotic string compactification on a Z(6) orbifold, Nucl. Phys. B 704 (2005) 3.

    Article  MathSciNet  ADS  Google Scholar 

  29. W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Supersymmetric standard model from the heterotic string, Phys. Rev. Lett. 96 (2006) 121602.

    Article  MathSciNet  ADS  Google Scholar 

  30. W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Supersymmetric standard model from the heterotic string. II, Nucl. Phys. B 785 (2007) 149.

    Article  ADS  Google Scholar 

  31. S. Förste, H.P. Nilles, P.K.S. Vaudrevange and A. Wingerter, Heterotic brane world, Phys. Rev. D 70 (2004) 106008.

    ADS  Google Scholar 

  32. T. Kobayashi, H.P. Nilles, F. Ploger, S. Raby and M. Ratz, Stringy origin of non-abelian discrete flavor symmetries, Nucl. Phys. B 768 (2007) 135.

    Article  MathSciNet  ADS  Google Scholar 

  33. P. Candelas, A.M. Dale, C.A. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nucl. Phys. B 298 (1988) 493.

    Article  ADS  Google Scholar 

  34. P. Candelas, C.A. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds. 2. Three generation manifolds, Nucl. Phys. B 306 (1988) 113.

    Article  ADS  Google Scholar 

  35. P.S. Green, T. Hubsch and C.A. Lütken, All Hodge numbers of all complete intersection Calabi-Yau manifolds, Class. Quant. Grav. 6 (1989) 105.

    Article  MATH  ADS  Google Scholar 

  36. A.-m. He and P. Candelas, On the number of complete intersection Calabi-Yau manifolds, Commun. Math. Phys. 135 (1990) 193.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  37. M. Gagnon and Q. Ho-Kim, An exhaustive list of complete intersection Calabi-Yau manifolds, Mod. Phys. Lett. A 9 (1994) 2235.

    MathSciNet  ADS  Google Scholar 

  38. P. Candelas and R. Davies, New Calabi-Yau Manifolds with small Hodge numbers, arXiv:0809.4681 [SPIRES].

  39. T. Hubsch, Calabi-Yau Manifolds — A bestiary for physicists, World Scientific, Singapore (1994).

    Google Scholar 

  40. J. Distler and B.R. Greene, Aspects of (2, 0) string compactifications, Nucl. Phys. B 304 (1988) 1.

    Article  MathSciNet  ADS  Google Scholar 

  41. S. Kachru, Some three generation (0, 2) Calabi-Yau models, Phys. Lett. B 349 (1995) 76.

    Article  MathSciNet  ADS  Google Scholar 

  42. M.R. Douglas and C.-g. Zhou, Chirality change in string theory, JHEP 06 (2004) 014.

    Article  MathSciNet  ADS  Google Scholar 

  43. L.B. Anderson, Y.H. He and A. Lukas, Algorithmic proofs of vector bundle stability, to appear.

  44. L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, Stability walls in heterotic theories, JHEP 09 (2009) 026.

    Article  Google Scholar 

  45. L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, The edge of supersymmetry: stability walls in heterotic theory, Phys. Lett. B 677 (2009) 190.

    MathSciNet  ADS  Google Scholar 

  46. L.B. Anderson, J. Gray, Y.H. He and A. Lukas, Compactifying on complete intersections, to appear.

  47. G. Horrocks and D. Mumford, A rank 2 vector bundle on \( {\mathbb{P}^4} \) with 15000 symmetries, Topology 12 (1973) 63.

    Article  MATH  MathSciNet  Google Scholar 

  48. A. Beilinson, Coherent sheaves on \( {\mathbb{P}^n} \) and problems in linear algebra, Funktsional. Anal. i Prilozhen. 12 (1978) 68.

    Article  MATH  MathSciNet  Google Scholar 

  49. M. Maruyama, Moduli of stable sheaves, II, J. Math. Kyoto Univ. 18 (1978) 557.

    MATH  MathSciNet  Google Scholar 

  50. C. Okonek, M. Schneider, H. Spindler, Vector bundles on complex projective spaces, Birkhauser Verlag, Germany (1988).

    Google Scholar 

  51. W. Fulton and R. Lazarsfeld, On the connectedness of degeneracy loci and special divisors, Acta Math. 146 (1981) 271.

    Article  MATH  MathSciNet  Google Scholar 

  52. K. Uhlenbeck and S.-T. Yau, On the existence of Hermitian Yang-Mills connections in stable bundles, Comm. Pure App. Math. 39 (1986) 257.

    Article  MATH  MathSciNet  Google Scholar 

  53. K. Uhlenbeck and S.-T. Yau, A note on our previous paper: on the existence of hermitian Yang-Mills connections in stable vector bundles, Comm. Pure App. Math. 42 (1986) 703.

    Article  MathSciNet  Google Scholar 

  54. S. Donaldson, Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. 3 (1985) 1.

    Article  MathSciNet  Google Scholar 

  55. M.C. Brambilla, Semistability of certain bundles on a quintic Calabi-Yau threefold, math.AG/0509599.

  56. D. Mumford, J. Fogarty and F. Kirwan, Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete volume 2, Springer-Verlag, Berlin Germany (1994).

    Google Scholar 

  57. F. Knop, H. Kraft, D. Luna and T. Vust, Local properties of algebraic group actions, in Algebraische Transformationsgruppen und Invariantentheorie, DMV Seminar 13, Birkhäuser, Basel Switzerland (1989).

    Google Scholar 

  58. R. Donagi, B.A. Ovrut, T. Pantev and R. Reinbacher, SU(4) instantons on Calabi-Yau threefolds with Z 2 × Z 2 fundamental group, JHEP 01 (2004) 022.

    Article  MathSciNet  ADS  Google Scholar 

  59. W. Fulton and J. Harris, Representation theory: a first course, Springer, New York U.S.A. (1991).

    MATH  Google Scholar 

  60. R. Hartshorne, Algebraic geometry, springer, Graduate Text in Mathematics volume 52, Springer-Verlag, Germany (1977).

    Google Scholar 

  61. P. Griffith and J. Harris, Principles of algebraic geometry, Wiley Interscience, U.S.A. (1978).

    Google Scholar 

  62. J.D. Breit, B.A. Ovrut and G.C. Segre, E 6 symmetry breaking in the superstring theory, Phys. Lett. B 158 (1985) 33.

    ADS  Google Scholar 

  63. V. Braun, Three generations on the quintic quotient, arXiv:0909.5682 [SPIRES].

  64. P. Candelas, X. de la Ossa, Y.-H. He and B. Szendroi, Triadophilia: a special corner in the landscape, Adv. Theor. Math. Phys. 12 (2008) 2.

    Google Scholar 

  65. V. Braun, B.A. Ovrut, T. Pantev and R. Reinbacher, Elliptic Calabi-Yau threefolds with Z(3) × Z(3) Wilson lines, JHEP 12 (2004) 062.

    Article  MathSciNet  ADS  Google Scholar 

  66. V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, Vector bundle extensions, sheaf cohomology and the heterotic standard model, Adv. Theor. Math. Phys. 10 (2006) 4.

    MathSciNet  Google Scholar 

  67. M. Ambroso and B. Ovrut, The B-L/electroweak hierarchy in heterotic string and M-theory, JHEP 10 (2009) 011.

    Article  Google Scholar 

  68. M. Ambroso and B.A. Ovrut, The B-L/electroweak hierarchy in smooth heterotic compactifications, arXiv:0910.1129 [SPIRES].

  69. V. Braun, P. Candelas and R. Davies, A three-generation Calabi-Yau manifold with small Hodge numbers, arXiv:0910.5464 [SPIRES].

  70. V. Braun, M. Kreuzer, B.A. Ovrut and E. Scheidegger, Worldsheet instantons and torsion curves. Part A: direct computation, JHEP 10 (2007) 022.

    Article  MathSciNet  ADS  Google Scholar 

  71. G.-M. Greuel, G. Pfister and H. Schönemann, Singular: a computer algebra system for polynomial computations, Centre for Computer Algebra, University of Kaiserslautern (2001), available at http://www.singular.uni-kl.de/.

  72. D.G. Grayson and M.E. Stillman, Macaulay2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2/.

  73. D.J.S. Robinson, A course in the theory of groups, Graduate Texts in Mathematics, Springer, New York U.S.A. (1995).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA, 19104-6395, U.S.A.

    Lara B. Anderson

  2. Rudolf Peierls Centre for Theoretical Physics, Oxford University, 1 Keble Road, Oxford, OX1 3NP, U.K.

    James Gray, Yang-Hui He & Andre Lukas

  3. Merton College, Oxford, OX1 4JD, U.K.

    Yang-Hui He

  4. Department of Mathematics, City University London, Northampton Square, London, EC1V 0HB, U.K.

    Yang-Hui He

Authors
  1. Lara B. Anderson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James Gray
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yang-Hui He
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andre Lukas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lara B. Anderson.

Additional information

ArXiv ePrint: 0911.1569

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anderson, L.B., Gray, J., He, YH. et al. Exploring positive monad bundles and a new heterotic standard model. J. High Energ. Phys. 2010, 54 (2010). https://doi.org/10.1007/JHEP02(2010)054

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2010)054

Keywords

Search

Navigation