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Communications in Mathematical Physics

, Volume 263, Issue 3, pp 711–722 | Cite as

Hamiltonian Perspective on Generalized Complex Structure

  • Maxim ZabzineEmail author
Article

Abstract

In this note we clarify the relation between extended world-sheet super-symmetry and generalized complex structure. The analysis is based on the phase space description of a wide class of sigma models. We point out the natural isomorphism between the group of orthogonal automorphisms of the Courant bracket and the group of local canonical transformations of the cotangent bundle of the loop space. Indeed this fact explains the natural relation between the world-sheet and the geometry of TT*. We discuss D-branes in this perspective.

Keywords

Neural Network Statistical Physic Phase Space Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alekseev, A., Strobl, T.: Current algebra and differential geometry. JHEP 0503, 035 (2005)CrossRefADSGoogle Scholar
  2. 2.
    Cattaneo, A.S., Felder, G.: A path integral approach to the Kontsevich quantization formula. Commun. Math. Phys. 212, 591 (2000)CrossRefADSzbMATHMathSciNetGoogle Scholar
  3. 3.
    Cattaneo, A.S., Felder, G.: Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model. Lett. Math. Phys. 69, 157 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Gualtieri, M.: Generalized complex geometry. Oxford University DPhil thesis, http://arxiv.org/list/math.DG/0401221, 2004Google Scholar
  5. 5.
    Hitchin, N.: Generalized Calabi-Yau manifolds. Q. J. Math. 54, no. 3, 281–308, (2003)Google Scholar
  6. 6.
    Hull, C.M.: Actions for (2,1) sigma models and strings. Nucl. Phys. B 509, 252 (1998)CrossRefADSzbMATHMathSciNetGoogle Scholar
  7. 7.
    Kapustin, A., Orlov, D.: Vertex algebras, mirror symmetry, and D-branes: The case of complex tori. Commun. Math. Phys. 233, 79 (2003)CrossRefADSzbMATHMathSciNetGoogle Scholar
  8. 8.
    Kapustin, A.: Topological strings on noncommutative manifolds. Int. J. Geom. Meth. Mod. Phys. 1, 49 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Kapustin, A., Li, Y.: Topological sigma-models with H-flux and twisted generalized complex. http://arxiv.org/list/hep-th/0407249, 2004Google Scholar
  10. 10.
    Lindström, U., Zabzine, M.: N = 2 boundary conditions for non-linear sigma models and Landau-Ginzburg models. JHEP 0302, 006 (2003)CrossRefADSGoogle Scholar
  11. 11.
    Lindström, U.: Generalized N = (2,2) supersymmetric non-linear sigma models. Phys. Lett. B 587, 216 (2004)CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Lindström, U., Minasian, R., Tomasiello, A., Zabzine, M.: Generalized complex manifolds and supersymmetry. Commun. Math. Phys. 257, 235 (2005)CrossRefADSzbMATHGoogle Scholar
  13. 13.
    Zabzine, M.: Geometry of D-branes for general N = (2,2) sigma models. Lett. Math. Phys. 70, 211 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Zucchini, R.: A sigma model field theoretic realization of Hitchin's generalized complex geometry. JHEP 0411, 045 (2004)CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    Zucchini, R.: Generalized complex geometry, generalized branes and the Hitchin sigma model. JHEP 0503, 022 (2005)CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.School of Mathematical SciencesQueen Mary, University of LondonLondonUK

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