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Geometry of D-branes for General N=(2,2) Sigma Models

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Abstract

We give a world-sheet description of D-brane in terms of gluing conditions on \(T {\cal M} \oplus T^{*} {\cal M}\) Using the notion of generalized Kähler geometry we show that A- and B-types D-branes for the general N=(2,2) supersymmetric sigma model (including a non-trivial NS-flux) correspond to the (twisted) generalized complex submanifolds with respect to the different (twisted) generalized complex structures however.

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References

  • C. Albertsson U. Lindström Zabzine M. (2003) ArticleTitleN =1 supersymmetric sigma model with boundaries. I. Commun Math. Phys. 233 403

    Google Scholar 

  • C. Albertsson U. Lindström M. Zabzine (2004) ArticleTitleN =1 supersymmetric sigma model with boundaries II Nucl. Phys. B. 678 295

    Google Scholar 

  • A.Y. Alekseev V. Schomerus (1999) ArticleTitleD-branes in the WZW model Phys. Rev. D. 60 061901

    Google Scholar 

  • Ben-Bassat O., Boyarchenko M. Submanifolds of generalized complex manifolds, arXiv:math.DG/0309013.

  • Ben-Bassat, O.: Mirror symmetry and generalized complex manifolds, arXiv:math.AG/0405303.

  • Bonechi, F. and Zabzine, M.: Poisson sigma model over group manifolds, arXiv:hepth/0311213.

  • Cattaneo, A. S. and Felder, G.: Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model, arXiv:math.qa/0309180.

  • G. Felder J. Frohlich J. Fuchs C. Schweigert (2000) ArticleTitleThe geometry of WZW branes J. Geom. Phys. 34 162

    Google Scholar 

  • Fidanza, S., Minasian, R. and Tomasiello, A.: Mirror symmetric SU(3)-structure manifolds with NS fluxes, arXiv:hep-th/0311122.

  • S.J. Gates C.M. Hull M. Ročcek (1984) ArticleTitleTwisted multiplets and new supersymmetric nonlinear sigma models Nucl. Phys. B 248 157 Occurrence Handle10.1016/0550-3213(84)90592-3

    Article  Google Scholar 

  • Gualtieri, M.: Generalized complex geometry, Oxford University DPhil thesis, arXiv:math.DG/0401221.

  • N. Hitchin (2003) ArticleTitleGeneralized Calabi Yau manifolds Q. J. Math. 54 IssueID3 281–308

    Google Scholar 

  • A. Kapustin D. Orlov (2003) ArticleTitleVertex algebras, mirror symmetry, and D-branes: The case of complex tori Commun. Math. Phys. 233 79 Occurrence Handle10.1007/s00220-002-0755-7 Occurrence Handle01903851

    Article  MATH  Google Scholar 

  • Kapustin, A. and Orlov, D.: Remarks on A-branes, mirror symmetry, and the Fukaya category, arXiv:hep-th/0109098.

  • Kapustin, A.: Topological strings on noncommutative manifolds, arXiv:hep-th/0310057

  • U. Lindström M. Zabzine (2003) ArticleTitleN =2 boundary conditions for non-linear sigma models and Landau-Ginzburg models JHEP 0302 006 Occurrence Handle10.1088/1126-6708/2003/02/006

    Article  Google Scholar 

  • U. Lindström M. Zabzine (2003) ArticleTitleD-branes in N =2 WZW models Phys. Lett. B 560 108 Occurrence Handle10.1016/S0370-2693(03)00332-0

    Article  Google Scholar 

  • Lindström, U., Minasian, R., Tomasiello, A. and Zabzine, M.: Generalized complex manifolds and supersymmetry, arXiv:hep-th/0405085.

  • S. Lyakhovich M. Zabzine (2002) ArticleTitlePoisson geometry of sigma models with extended supersymmetry Phys. Lett. B. 548 243

    Google Scholar 

  • H. Ooguri Y. Oz Z. Yin (1996) ArticleTitleD-branes on Calabi-Yau spaces and their mirrors Nucl. Phys. B. 477 407

    Google Scholar 

  • S. Stanciu (2000) ArticleTitleD-branes in group manifolds JHEP. 0001 025

    Google Scholar 

Download references

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Authors and Affiliations

  1. Lab. de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Paris VI, 4 Place Jussieu, 75252, Paris Cedex 05, France

    Maxim Zabzine

  2. Institut Mittag-Leffler, Auravägen 17, S-182 62, Djursholm, Sweden

    Maxim Zabzine

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  1. Maxim Zabzine
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Correspondence to Maxim Zabzine.

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Mathematics Subject Classifications (2000). 81T30, 81T60, 81T40.

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Zabzine, M. Geometry of D-branes for General N=(2,2) Sigma Models. Lett Math Phys 70, 211–221 (2004). https://doi.org/10.1007/s11005-004-4296-1

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