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Journal of High Energy Physics

, 2010:74 | Cite as

Heterotic compactifications on nearly Kähler manifolds

  • Olaf LechtenfeldEmail author
  • Christoph Nölle
  • Alexander D. Popov
Article

Abstract

We consider compactifications of heterotic supergravity on anti-de Sitter space, with a six-dimensional nearly Kähler manifold as the internal space. Completing the model proposed by Frey and Lippert [10] with the particular choice of SU(3)/U(1) × U(1) for the internal manifold, we show that it satisfies not only the supersymmetry constraints but also the equations of motion with string corrections of order α′. Furthermore, we present a nonsupersymmetric model. In both solutions we find confirmed a recent result of Ivanov [18] on the connection used for anomaly cancellation. Interestingly, the volume of the internal space is fixed by the supersymmetry constraints and/or the equations of motion.

Keywords

Flux compactifications Superstring Vacua Differential and Algebraic Geometry 

References

  1. [1]
    A. Bachelot, The Dirac system on the Anti-de Sitter Universe, Commun. Math. Phys. 283 (2008) 127 [arXiv:0706.1315] [SPIRES].MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. [2]
    H. Baum, Twistor spinors on Lorentzian symmetric spaces, math.DG/9803089.
  3. [3]
    K. Becker and S. Sethi, Torsional heterotic geometries, Nucl. Phys. B 820 (2009) 1 [arXiv:0903.3769] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    E.A. Bergshoeff and M. de Roo, The quartic effective action of the heterotic string and supersymmetry, Nucl. Phys. B 328 (1989) 439 [SPIRES].ADSzbMATHCrossRefGoogle Scholar
  5. [5]
    C. Bohle, Killing and twistor spinors on Lorentzian manifolds, http://www.math.tu-berlin.de/∼bohle/pub/dipl.dvi.
  6. [6]
    J.-B. Butruille, Homogeneous nearly Kähler manifolds, math/0612655.
  7. [7]
    G. Lopes Cardoso, G. Curio, G. Dall’Agata and D. Lüst, Heterotic string theory on non-Kähler manifolds with H-flux and gaugino condensate, Fortsch. Phys. 52 (2004) 483 [hep-th/0310021] [SPIRES].ADSCrossRefGoogle Scholar
  8. [8]
    G. Lopes Cardoso et al., Non-Kähler string backgrounds and their five torsion classes, Nucl. Phys. B 652 (2003) 5 [hep-th/0211118] [SPIRES].ADSCrossRefGoogle Scholar
  9. [9]
    M. Fernandez, S. Ivanov, L. Ugarte and R. Villacampa, Non-Kähler heterotic string compactifications with non-zero fluxes and constant dilaton, Commun. Math. Phys. 288 (2009) 677 [arXiv:0804.1648] [SPIRES].MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. [10]
    A.R. Frey and M. Lippert, AdS strings with torsion: non-complex heterotic compactifications, Phys. Rev. D 72 (2005) 126001 [hep-th/0507202] [SPIRES].MathSciNetADSGoogle Scholar
  11. [11]
    T. Friedrich, On types of non-integrable geometries, math/0205149.
  12. [12]
    J.-X. Fu and S.-T. Yau, The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation, J. Diff. Geom. 78 (2009) 369 [hep-th/0604063] [SPIRES].MathSciNetGoogle Scholar
  13. [13]
    T.R. Govindarajan, A.S. Joshipura, S.D. Rindani and U. Sarkar, Supersymmetric compactification of the heterotic string on coset spaces, Phys. Rev. Lett. 57 (1986) 2489 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    M.B. Green, J.H. Schwarz and E. Witten, Superstring theory, Vol. 2: Loop amplitudes, anomalies & phenomenology, Cambridge University Press (1987).Google Scholar
  15. [15]
    R. Grunewald, Six-dimensional Riemannian manifolds with a real Killing spinor, Ann. Global Anal. Geom. 8 (1990) 43. MathSciNetzbMATHCrossRefGoogle Scholar
  16. [16]
    D. Harland, T.A. Ivanova, O. Lechtenfeld and A.D. Popov, Yang-Mills flows on nearly Kähler manifolds and G 2 -instantons, arXiv:0909.2730 [SPIRES].
  17. [17]
    C.M. Hull, Anomalies, ambiguities and superstrings, Phys. Lett. B 167 (1986) 51 [SPIRES].MathSciNetADSGoogle Scholar
  18. [18]
    S. Ivanov, Heterotic supersymmetry, anomaly cancellation and equations of motion, Phys. Lett. B 685 (2010) 190 [arXiv:0908.2927] [SPIRES].ADSGoogle Scholar
  19. [19]
    S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. 1, John Wiley & Sons (1963).Google Scholar
  20. [20]
    J. Li and S.-T. Yau, The existence of supersymmetric string theory with torsion, J. Diff. Geom. 70 (2005) 143 [hep-th/0411136] [SPIRES].MathSciNetzbMATHGoogle Scholar
  21. [21]
    P. Manousselis, N. Prezas and G. Zoupanos, Supersymmetric compactifications of heterotic strings with fluxes and condensates, Nucl. Phys. B 739 (2006) 85 [hep-th/0511122] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    J. Polchinski, String theory, Vol. I, Cambridge University Press (2005).Google Scholar
  23. [23]
    A.D. Popov, Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kähler and nearly Calabi-Yau twistor 6-manifolds, Nucl. Phys. B 828 (2010) 594 [arXiv:0907.0106] [SPIRES].ADSCrossRefGoogle Scholar
  24. [24]
    A. Strominger, Superstrings with torsion, Nucl. Phys. B 274 (1986) 253 [SPIRES]. MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    L. Ugarte and R. Villacampa, Non-nilpotent complex geometry of nilmanifolds and heterotic supersymmetry, arXiv:0912.5110.

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Olaf Lechtenfeld
    • 1
    • 2
    Email author
  • Christoph Nölle
    • 1
  • Alexander D. Popov
    • 3
  1. 1.Institut für Theoretische PhysikLeibniz Universität HannoverHannoverGermany
  2. 2.Centre for Quantum Engineering and Space-Time ResearchLeibniz Universität HannoverHannoverGermany
  3. 3.Bogoliubov Laboratory of Theoretical PhysicsJINRDubna, Moscow RegionRussia

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