Letters in Mathematical Physics

, Volume 70, Issue 3, pp 211–221 | Cite as

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



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.


string theory D-branes generalized complex theory 


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  1. Albertsson, C., Lindström, U., Zabzine, , M.,  2003N =1 supersymmetric sigma model with boundaries.I. Commun Math. Phys.233403[arXiv:hepth/0111161].Google Scholar
  2. Albertsson, C., Lindström, U., Zabzine, M. 2004N =1 supersymmetric sigma model with boundaries IINucl. Phys. B.678295[arXiv:hep-th/0202069]Google Scholar
  3. Alekseev, A.Y., Schomerus, V. 1999D-branes in the WZW modelPhys. Rev. D.60061901[arXiv:hep-th/9812193]Google Scholar
  4. Ben-Bassat O., Boyarchenko M. Submanifolds of generalized complex manifolds, arXiv:math.DG/0309013.Google Scholar
  5. Ben-Bassat, O.: Mirror symmetry and generalized complex manifolds, arXiv:math.AG/0405303.Google Scholar
  6. Bonechi, F. and Zabzine, M.: Poisson sigma model over group manifolds, arXiv:hepth/0311213.Google Scholar
  7. Cattaneo, A. S. and Felder, G.: Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model, arXiv:math.qa/0309180.Google Scholar
  8. Felder, G., Frohlich, J., Fuchs, J., Schweigert, C. 2000The geometry of WZW branesJ. Geom. Phys.34162[arXiv:hep-th/9909030].Google Scholar
  9. Fidanza, S., Minasian, R. and Tomasiello, A.: Mirror symmetric SU(3)-structure manifolds with NS fluxes, arXiv:hep-th/0311122.Google Scholar
  10. Gates, S.J., Hull, C.M., Ročcek, M. 1984Twisted multiplets and new supersymmetric nonlinear sigma modelsNucl. Phys. B248157CrossRefGoogle Scholar
  11. Gualtieri, M.: Generalized complex geometry, Oxford University DPhil thesis, arXiv:math.DG/0401221.Google Scholar
  12. Hitchin, N. 2003Generalized Calabi Yau manifoldsQ. J. Math.54281308arXiv:math.DG/0209099.Google Scholar
  13. Kapustin, A., Orlov, D. 2003Vertex algebras, mirror symmetry, and D-branes: The case of complex toriCommun. Math. Phys.23379[arXiv:hep-th/0010293]CrossRefMATHGoogle Scholar
  14. Kapustin, A. and Orlov, D.: Remarks on A-branes, mirror symmetry, and the Fukaya category, arXiv:hep-th/0109098.Google Scholar
  15. Kapustin, A.: Topological strings on noncommutative manifolds, arXiv:hep-th/0310057Google Scholar
  16. Lindström, U., Zabzine, M. 2003N =2 boundary conditions for non-linear sigma models and Landau-Ginzburg modelsJHEP0302006[arXiv:hep-th/0209098]CrossRefGoogle Scholar
  17. Lindström, U., Zabzine, M. 2003D-branes in N =2 WZW modelsPhys. Lett. B560108[arXiv:hep-th/0212042]CrossRefGoogle Scholar
  18. Lindström, U., Minasian, R., Tomasiello, A. and Zabzine, M.: Generalized complex manifolds and supersymmetry, arXiv:hep-th/0405085.Google Scholar
  19. Lyakhovich, S., Zabzine, M. 2002Poisson geometry of sigma models with extended supersymmetryPhys. Lett. B.548243[arXiv:hep-th/0210043]Google Scholar
  20. Ooguri, H., Oz, Y., Yin, Z. 1996D-branes on Calabi-Yau spaces and their mirrorsNucl. Phys. B.477407[arXiv:hep-th/9606112]Google Scholar
  21. Stanciu, S. 2000D-branes in group manifoldsJHEP.0001025[arXiv:hepth/9909163]Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Lab. de Physique Théorique et Hautes EnergiesUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.Institut Mittag-LefflerDjursholmSweden

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