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Nearly Kähler heterotic compactifications with fermion condensates

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Abstract

We revisit AdS4 heterotic compactifications on nearly Kähler manifolds in the presence of H-flux and certain fermion condensates. Unlike previous studies, we do not assume the vanishing of the supersymmetry variations. Instead we determine the full equations of motion originating from the ten-dimensional action, and subsequently we provide explicit solutions to them on nearly Kähler manifolds at first order in α′. The Bianchi identity is also taken into account in order to guarantee the absence of all anomalies. In the presence of H-flux, which is identified with the torsion of the internal space, as well as of fermion condensates in the gaugino and dilatino sectors, new solutions are determined. These solutions provide a full classification of consistent backgrounds of heterotic supergravity under our assumptions. All the new solutions are non-supersymmetric, while previously known supersymmetric ones are recovered too. Our results indicate that fully consistent (supersymmetric or not) heterotic vacua on nearly Kähler manifolds are scarce, even on AdS4, and they can be completely classified.

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References

  1. A. Strominger, Superstrings with Torsion, Nucl. Phys. B 274 (1986) 253 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. G. Lopes Cardoso, G. Curio, G. Dall’Agata, D. Lüst, P. Manousselis and G. Zoupanos, NonKähler string backgrounds and their five torsion classes, Nucl. Phys. B 652 (2003) 5 [hep-th/0211118] [INSPIRE].

    Article  ADS  Google Scholar 

  3. M. Dine, R. Rohm, N. Seiberg and E. Witten, Gluino Condensation in Superstring Models, Phys. Lett. B 156 (1985) 55 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  4. J. Derendinger, L.E. Ibáñez and H.P. Nilles, On the Low-Energy D = 4, N = 1 Supergravity Theory Extracted from the D = 10, N = 1 Superstring, Phys. Lett. B 155 (1985) 65 [INSPIRE].

    ADS  Google Scholar 

  5. G. Lopes Cardoso, G. Curio, G. Dall’Agata and D. Lüst, Heterotic string theory on nonKähler manifolds with H flux and gaugino condensate, Fortsch. Phys. 52 (2004) 483 [hep-th/0310021] [INSPIRE].

    Article  ADS  Google Scholar 

  6. A.R. Frey and M. Lippert, AdS strings with torsion: Non-complex heterotic compactifications, Phys. Rev. D 72 (2005) 126001 [hep-th/0507202] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  7. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. S. Ivanov, Heterotic supersymmetry, anomaly cancellation and equations of motion, Phys. Lett. B 685 (2010) 190 [arXiv:0908.2927] [INSPIRE].

    ADS  Google Scholar 

  9. O. Lechtenfeld, C. Nolle and A.D. Popov, Heterotic compactifications on nearly Kähler manifolds, JHEP 09 (2010) 074 [arXiv:1007.0236] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. E. Bergshoeff, M. de Roo, B. de Wit and P. van Nieuwenhuizen, Ten-Dimensional Maxwell-Einstein Supergravity, Its Currents and the Issue of Its Auxiliary Fields, Nucl. Phys. B 195 (1982) 97 [INSPIRE].

    Article  ADS  Google Scholar 

  11. G. Chapline and N. Manton, Unification of Yang-Mills Theory and Supergravity in Ten-Dimensions, Phys. Lett. B 120 (1983) 105 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  12. E. Bergshoeff and M. de Roo, The Quartic Effective Action Of The Heterotic String And Supersymmetry, Nucl. Phys. B 328 (1989) 439 [INSPIRE].

    Article  ADS  Google Scholar 

  13. K. Becker and S. Sethi, Torsional Heterotic Geometries, Nucl. Phys. B 820 (2009) 1 [arXiv:0903.3769] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. M. Graña, Flux compactifications in string theory: A Comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].

    Article  ADS  Google Scholar 

  15. S.R. Green, E.J. Martinec, C. Quigley and S. Sethi, Constraints on String Cosmology, Class. Quant. Grav. 29 (2012) 075006 [arXiv:1110.0545] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. J.-B. Butruille, Homogeneous nearly Kähler manifolds, arXiv:math/0612655.

  17. L. Castellani, L. Romans and N. Warner, Symmetries Of Coset Spaces And Kaluza-klein Supergravity, Annals Phys. 157 (1984) 394 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. F. Mueller-Hoissen and R. Stuckl, Coset Spaces And Ten-dimensional Unified Theories, Class. Quant. Grav. 5 (1988) 27 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  19. 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] [INSPIRE].

    Article  ADS  Google Scholar 

  20. H. Baum, Twistor spinors on Lorentzian symmetric spaces, math/9803089.

  21. P. Manousselis and G. Zoupanos, Dimensional reduction over coset spaces and supersymmetry breaking, JHEP 03 (2002) 002 [hep-ph/0111125] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. F. Farakos, A. Kehagias and E.N. Saridakis, Vanishing Cosmological Constant by Gravitino-Dressed Compactification of 1 1D Supergravity, JHEP 12 (2011) 107 [arXiv:1111.1577] [INSPIRE].

    Article  ADS  Google Scholar 

  23. M. Klaput, A. Lukas and C. Matti, Bundles over Nearly-Kähler Homogeneous Spaces in Heterotic String Theory, JHEP 09 (2011) 100 [arXiv:1107.3573] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. A. Chatzistavrakidis, P. Manousselis and G. Zoupanos, Reducing the Heterotic Supergravity on nearly-Kähler coset spaces, Fortsch. Phys. 57 (2009) 527 [arXiv:0811.2182] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. A. Chatzistavrakidis and G. Zoupanos, Dimensional Reduction of the Heterotic String over nearly-Kähler manifolds, JHEP 09 (2009) 077 [arXiv:0905.2398] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. B. de Carlos, S. Gurrieri, A. Lukas and A. Micu, Moduli stabilisation in heterotic string compactifications, JHEP 03 (2006) 005 [hep-th/0507173] [INSPIRE].

    Article  Google Scholar 

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Authors and Affiliations

  1. Bethe Center for Theoretical Physics and Physikalisches Institut der Universität Bonn, Nussallee 12, D-53115, Bonn, Germany

    Athanasios Chatzistavrakidis

  2. Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany

    Olaf Lechtenfeld

  3. Centre for Quantum Engineering and Space-Time Research, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Olaf Lechtenfeld

  4. Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Moscow Region, Russia

    Alexander D. Popov

Authors
  1. Athanasios Chatzistavrakidis
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  2. Olaf Lechtenfeld
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  3. Alexander D. Popov
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Correspondence to Olaf Lechtenfeld.

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ArXiv ePrint: 1202.1278

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Chatzistavrakidis, A., Lechtenfeld, O. & Popov, A.D. Nearly Kähler heterotic compactifications with fermion condensates. J. High Energ. Phys. 2012, 114 (2012). https://doi.org/10.1007/JHEP04(2012)114

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  • DOI: https://doi.org/10.1007/JHEP04(2012)114

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