A brief review of supersymmetric non-linear sigma models and generalized complex geometry

Ulf Lindström

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 5, page 307-318
  • ISSN: 0044-8753

Abstract

top
This is a review of the relation between supersymmetric non-linear sigma models and target space geometry. In particular, we report on the derivation of generalized Kähler geometry from sigma models with additional spinorial superfields. Some of the results reviewed are: Generalized complex geometry from sigma models in the Lagrangian formulation; Coordinatization of generalized Kähler geometry in terms of chiral, twisted chiral and semi-chiral superfields; Generalized Kähler geometry from sigma models in the Hamiltonian formulation.

How to cite

top

Lindström, Ulf. "A brief review of supersymmetric non-linear sigma models and generalized complex geometry." Archivum Mathematicum 042.5 (2006): 307-318. <http://eudml.org/doc/249819>.

@article{Lindström2006,
abstract = {This is a review of the relation between supersymmetric non-linear sigma models and target space geometry. In particular, we report on the derivation of generalized Kähler geometry from sigma models with additional spinorial superfields. Some of the results reviewed are: Generalized complex geometry from sigma models in the Lagrangian formulation; Coordinatization of generalized Kähler geometry in terms of chiral, twisted chiral and semi-chiral superfields; Generalized Kähler geometry from sigma models in the Hamiltonian formulation.},
author = {Lindström, Ulf},
journal = {Archivum Mathematicum},
keywords = {sigma model; generalized Kähler geometry; generalized complex geometry; superfield},
language = {eng},
number = {5},
pages = {307-318},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A brief review of supersymmetric non-linear sigma models and generalized complex geometry},
url = {http://eudml.org/doc/249819},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Lindström, Ulf
TI - A brief review of supersymmetric non-linear sigma models and generalized complex geometry
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 307
EP - 318
AB - This is a review of the relation between supersymmetric non-linear sigma models and target space geometry. In particular, we report on the derivation of generalized Kähler geometry from sigma models with additional spinorial superfields. Some of the results reviewed are: Generalized complex geometry from sigma models in the Lagrangian formulation; Coordinatization of generalized Kähler geometry in terms of chiral, twisted chiral and semi-chiral superfields; Generalized Kähler geometry from sigma models in the Hamiltonian formulation.
LA - eng
KW - sigma model; generalized Kähler geometry; generalized complex geometry; superfield
UR - http://eudml.org/doc/249819
ER -

References

top
  1. Albertsson C., Lindström U., Zabzine M., N = 1 supersymmetric sigma model with boundaries. I, Comm. Math. Phys. 233, 403 (2003) [arXiv:hep-th/0111161]. Zbl1028.81044MR1962116
  2. Albertsson C., Lindström U., Zabzine M., N = 1 supersymmetric sigma model with boundaries. II, Nuclear Phys. B 678, 295 (2004) [arXiv:hep-th/0202069]. Zbl1097.81548MR2022994
  3. Alekseev A., Strobl T., Current algebra and differential geometry, JHEP 0503 (2005), 035 [arXiv:hep-th/0410183]. MR2151966
  4. Alvarez-Gaumé L., Freedman D. Z., Geometrical structure and ultraviolet finiteness in the supersymmetric sigma model, Comm. Math. Phys. 80, 443 (1981) (1981) MR0626710
  5. Bergamin L., Generalized complex geometry and the Poisson sigma model, Modern Phys. Lett. A 20, 985 (2005) [arXiv:hep-th/0409283]. Zbl1067.81046MR2148015
  6. Bredthauer A., Lindström U., Persson J., Zabzine M., Generalized Kaehler geometry from supersymmetric sigma models, arXiv:hep-th/0603130. Zbl1105.53053MR2260375
  7. Bredthauer A., Lindström U., Persson J., First-order supersymmetric sigma models and target space geometry, JHEP 0601, 144 (2006) [arXiv:hep-th/0508228]. MR2200293
  8. Buscher T., Lindström U., Roček M., New supersymmetric sigma models with Wess-Zumino terms, Phys. Lett. B202, 94 (1988). (1988) MR0930852
  9. Calvo I., Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry, arXiv:hep-th/0511179. Zbl1105.53063MR2247462
  10. Gates S. J., Hull C. M., Roček M., Twisted multiplets and new supersymmetric nonlinear sigma models, Nuclear Phys. B248 (1984) 157. (1984) 
  11. Grisaru M. T., Massar M., Sevrin A., Troost J., The quantum geometry of N = ( 2 , 2 ) non-linear sigma-models, Phys. Lett. B412, 53 (1997) [arXiv:hep-th/9706218]. (1997) MR1603804
  12. Gualtieri M., Generalized complex geometry, Oxford University DPhil thesis, [arXiv:math. DG/0401221]. Zbl1235.32020MR2811595
  13. Hitchin N., Generalized Calabi-Yau manifolds, Quart. J. Math. 54, No. 3 (2003), 281–308, [arXiv:math.DG/0209099]. Zbl1076.32019MR2013140
  14. Hitchin N., Instantons, Poisson structures and generalized Kähler geometry, [arXiv:math. DG/0503432]. Zbl1110.53056MR2217300
  15. Howe P. S., Sierra G., Two-dimensional supersymmetric nonlinear sigma models with torsion, Phys. Lett. B148, 451 (1984). (1984) MR0769268
  16. Howe P. S., Lindström U., Wulff L., Superstrings with boundary fermions, JHEP 0508, 041 (2005) [arXiv:hep-th/0505067]. MR2165805
  17. Howe P. S., Lindström U., Stojevic V., Special holonomy sigma models with boundaries, JHEP 0601, 159 (2006) [arXiv:hep-th/0507035]. MR2200283
  18. Ivanov I. T., Kim B. B., Roček M., Complex structures, duality and WZW models in extended superspace, Phys. Lett. B343 (1995) 133 [arXiv:hep-th/9406063]. (1995) MR1315282
  19. Kapustin A., Topological strings on noncommutative manifolds, Int. J. Geom. Methods Mod. Phys. 1 (2004) 49 [arXiv:hep-th/0310057]. Zbl1065.81108MR2055289
  20. Kapustin A., Li Y., Topological sigma-models with H-flux and twisted generalized complex manifolds, arXiv:hep-th/0407249. Zbl1192.81310MR2322555
  21. Lindström U., Rocek M., van Nieuwenhuizen P., Consistent boundary conditions for open strings, Nuclear Phys. B 662, 147 (2003) [arXiv:hep-th/0211266]. Zbl1027.83027MR1984375
  22. Lindström U., Zabzine M., N=2 Boundary conditions for non-linear sigma models and Landau-Ginzburg models, JHEP 0302, 006 (2003) [arXiv:hep-th/0209098]. MR1976901
  23. Lindström U., Generalized N = ( 2 , 2 ) supersymmetric non-linear sigma models, Phys. Lett. B587, 216 (2004) [arXiv:hep-th/0401100]. MR2065031
  24. Lindström U., Minasian R., Tomasiello A., Zabzine M., Generalized complex manifolds and supersymmetry, Comm. Math. Phys. 257, 235 (2005) [arXiv:hep-th/0405085]. Zbl1118.53048MR2163575
  25. Lindström U., Roček M., von Unge R., Zabzine M., Generalized Kaehler geometry and manifest N = ( 2 , 2 ) supersymmetric nonlinear sigma-models, JHEP 0507 (2005) 067 [arXiv:hep-th/0411186]. MR2163246
  26. Lindström U., Rocek M., von Unge R., Zabzine M., Generalized Kaehler manifolds and off-shell supersymmetry, arXiv:hep-th/0512164. Zbl1114.81077
  27. Lyakhovich S., Zabzine M., Poisson geometry of sigma models with extended supersymmetry, Phys. Lett. B548 (2002) 243 [arXiv:hep-th/0210043]. Zbl0999.81044MR1948542
  28. Pestun V., Topological strings in generalized complex space, arXiv:hep-th/0603145. Zbl1154.81024MR2322532
  29. Sevrin A., Troost J., Off-shell formulation of N = 2 non-linear sigma-models, Nuclear Phys. B492 (1997) 623 [arXiv:hep-th/9610102]. (1997) MR1456119
  30. Zabzine M., Hamiltonian perspective on generalized complex structure, arXiv:hep-th/0502137, to appear in Comm. Math. Phys. Zbl1104.53077MR2211820
  31. Zucchini R., A sigma model field theoretic realization of Hitchin’s generalized complex geometry, JHEP 0411 (2004) 045 [arXiv:hep-th/0409181]. MR2119918
  32. Zumino B., Supersymmetry and Kahler manifolds, Phys. Lett. B 87, 203 (1979). (1979) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.