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Non-commutative/non-associative IIA (IIB) geometries from Q- and R-branes and their intersections

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Abstract

In this paper we discuss the construction of non-geometric Q- and R-branes as sources of non-geometric Q- and R-fluxes in string compactifications. The non-geometric Q-branes, being obtained via T-duality from the NS 5-brane or respectively from the KK-monopole, are still local solutions of the standard NS action, where however the background fields G and B possess non-geometric global monodromy properties. We show that using double field theory and redefined background fields \( \widetilde{G} \) and β as well as their corresponding effective action, the Q-branes are locally and globally well behaved solutions. Furthermore the R-brane solution can be at least formally constructed using dual coordinates. We derive the associated non-geometric Q- and R-fluxes and discuss that closed strings moving in the space transversal to the world-volumes of the non-geometric branes see a non-commutative or a non-associative geometry.

In the second part of the paper we construct intersecting Q- and R-brane configurations as completely supersymmetric solutions of type IIA/B supergravity with certain SU(3) × SU(3) group structures. In the near horizon limit the intersecting brane configurations lead to type II backgrounds of the form AdS 4 × M 6, where the six-dimensional compact space M 6 is a torus fibration with various non-geometric Q- and R-fluxes in the compact directions. It exhibits an interesting non-commutative and non-associate geometric structure. Furthermore we also determine some of the effective four-dimensional superpotentials originating from the non-geometric fluxes.

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References

  1. W. Lerche, D. Lüst and A. Schellekens, Chiral Four-Dimensional Heterotic Strings from Selfdual Lattices, Nucl. Phys. B 287 (1987) 477 [INSPIRE].

    Article  ADS  Google Scholar 

  2. H. Kawai, D.C. Lewellen and S.H. Tye, Construction of Four-Dimensional Fermionic String Models, Phys. Rev. Lett. 57 (1986) 1832 [Erratum ibid. 58 (1987) 429] [INSPIRE].

  3. I. Antoniadis, C. Bachas and C. Kounnas, Four-Dimensional Superstrings, Nucl. Phys. B 289 (1987) 87 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. K. Narain, M. Sarmadi and C. Vafa, Asymmetric Orbifolds, Nucl. Phys. B 288 (1987) 551 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. S. Hellerman, J. McGreevy and B. Williams, Geometric constructions of nongeometric string theories, JHEP 01 (2004) 024 [hep-th/0208174] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. A. Dabholkar and C. Hull, Duality twists, orbifolds and fluxes, JHEP 09 (2003) 054 [hep-th/0210209] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. C. Hull, A Geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. C. Hull and B. Zwiebach, The Gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. D. Andriot, M. Larfors, D. Lüst and P. Patalong, A ten-dimensional action for non-geometric fluxes, JHEP 09 (2011) 134 [arXiv:1106.4015] [INSPIRE].

    Article  ADS  Google Scholar 

  14. D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, A geometric action for non-geometric fluxes, Phys. Rev. Lett. 108 (2012) 261602 [arXiv:1202.3060] [INSPIRE].

    Article  ADS  Google Scholar 

  15. D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, Non-Geometric Fluxes in Supergravity and Double Field Theory, Fortsch. Phys. 60 (2012) 1150 [arXiv:1204.1979] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  16. R. Blumenhagen, A. Deser, E. Plauschinn and F. Rennecke, A bi-invariant Einstein-Hilbert action for the non-geometric string, Phys. Lett. B 720 (2013) 215 [arXiv:1210.1591] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. R. Blumenhagen, A. Deser, E. Plauschinn and F. Rennecke, Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids, JHEP 02 (2013) 122 [arXiv:1211.0030] [INSPIRE].

    Article  ADS  Google Scholar 

  18. R. Blumenhagen and E. Plauschinn, Nonassociative Gravity in String Theory?, J. Phys. A 44 (2011) 015401 [arXiv:1010.1263] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  19. D. Lüst, T-duality and closed string non-commutative (doubled) geometry, JHEP 12 (2010) 084 [arXiv:1010.1361] [INSPIRE].

    Article  Google Scholar 

  20. R. Blumenhagen, A. Deser, D. Lüst, E. Plauschinn and F. Rennecke, Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry, J. Phys. A 44 (2011) 385401 [arXiv:1106.0316] [INSPIRE].

    ADS  Google Scholar 

  21. C. Condeescu, I. Florakis and D. Lüst, Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory, JHEP 04 (2012) 121 [arXiv:1202.6366] [INSPIRE].

    Article  ADS  Google Scholar 

  22. D. Andriot, M. Larfors, D. Lüst and P. Patalong, (Non-)commutative closed string on T-dual toroidal backgrounds, JHEP 06 (2013) 021 [arXiv:1211.6437] [INSPIRE].

    Article  ADS  Google Scholar 

  23. D. Mylonas, P. Schupp and R.J. Szabo, Membrane σ-models and Quantization of Non-Geometric Flux Backgrounds, JHEP 09 (2012) 012 [arXiv:1207.0926] [INSPIRE].

    Article  ADS  Google Scholar 

  24. E. Lozano-Tellechea and T. Ortin, 7-branes and higher Kaluza-Klein branes, Nucl. Phys. B 607 (2001) 213 [hep-th/0012051] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. E.A. Bergshoeff, T. Ortin and F. Riccioni, Defect Branes, Nucl. Phys. B 856 (2012) 210 [arXiv:1109.4484] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. J. de Boer and M. Shigemori, Exotic branes and non-geometric backgrounds, Phys. Rev. Lett. 104 (2010) 251603 [arXiv:1004.2521] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. J. de Boer and M. Shigemori, Exotic Branes in String Theory, arXiv:1209.6056 [INSPIRE].

  28. C. Kounnas, D. Lüst, P.M. Petropoulos and D. Tsimpis, AdS4 flux vacua in type-II superstrings and their domain-wall solutions, JHEP 09 (2007) 051 [arXiv:0707.4270] [INSPIRE].

    Article  ADS  Google Scholar 

  29. C. Caviezel et al., The Effective theory of type IIA AdS 4 compactifications on nilmanifolds and cosets, Class. Quant. Grav. 26 (2009) 025014 [arXiv:0806.3458] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. S. Jensen, The KK-Monopole/NS5-Brane in Doubled Geometry, JHEP 07 (2011) 088 [arXiv:1106.1174] [INSPIRE].

    Article  ADS  Google Scholar 

  31. J.-P. Derendinger, C. Kounnas, P.M. Petropoulos and F. Zwirner, Superpotentials in IIA compactifications with general fluxes, Nucl. Phys. B 715 (2005) 211 [hep-th/0411276] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. G. Villadoro and F. Zwirner, N=1 effective potential from dual type- IIA D6/O6 orientifolds with general fluxes, JHEP 06 (2005) 047 [hep-th/0503169] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  34. P.G. Camara, A. Font and L. Ibáñez, Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold, JHEP 09 (2005) 013 [hep-th/0506066] [INSPIRE].

    Article  ADS  Google Scholar 

  35. G. Dall’Agata, N. Prezas, H. Samtleben and M. Trigiante, Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds, Nucl. Phys. B 799 (2008) 80 [arXiv:0712.1026] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of Double Field Theory, JHEP 11 (2011) 052 [Erratum ibid. 1111 (2011) 109] [arXiv:1109.0290] [INSPIRE].

  37. T. Buscher, A Symmetry of the String Background Field Equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  38. T. Buscher, Path Integral Derivation of Quantum Duality in Nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  39. S. Gurrieri, J. Louis, A. Micu and D. Waldram, Mirror symmetry in generalized Calabi-Yau compactifications, Nucl. Phys. B 654 (2003) 61 [hep-th/0211102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. 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 

  41. N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser. 54 (2003) 281 [math/0209099] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  42. M. Gualtieri, Generalized complex geometry, math/0401221 [INSPIRE].

  43. M. Graña, R. Minasian, M. Petrini and A. Tomasiello, Generalized structures of N = 1 vacua, JHEP 11 (2005) 020 [hep-th/0505212] [INSPIRE].

    Article  ADS  Google Scholar 

  44. D. Lüst and D. Tsimpis, Supersymmetric AdS 4 compactifications of IIA supergravity, JHEP 02 (2005) 027 [hep-th/0412250] [INSPIRE].

    Article  Google Scholar 

  45. M. Graña, R. Minasian, M. Petrini and A. Tomasiello, A Scan for new N = 1 vacua on twisted tori, JHEP 05 (2007) 031 [hep-th/0609124] [INSPIRE].

    Article  ADS  Google Scholar 

  46. M. Graña, R. Minasian, M. Petrini and D. Waldram, T-duality, Generalized Geometry and Non-Geometric Backgrounds, JHEP 04 (2009) 075 [arXiv:0807.4527] [INSPIRE].

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Arnold-Sommerfeld-Center for Theoretical Physics, Fakultät für Physik, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333, München, Germany

    Falk Haßler & Dieter Lüst

  2. Max-Planck-Institut für Physik, Föhringer Ring 6, 80805, München, Germany

    Falk Haßler & Dieter Lüst

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  1. Falk Haßler
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  2. Dieter Lüst
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Correspondence to Dieter Lüst.

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ArXiv ePrint: 1303.1413

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Haßler, F., Lüst, D. Non-commutative/non-associative IIA (IIB) geometries from Q- and R-branes and their intersections. J. High Energ. Phys. 2013, 48 (2013). https://doi.org/10.1007/JHEP07(2013)048

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