×
Bredthauer, Andreas; Lindström, Ulf; Persson, Jonas; Zabzine, Maxim

Generalized Kähler geometry from supersymmetric sigma models. (English) Zbl 1105.53053

Lett. Math. Phys. 77, No. 3, 291-308 (2006).
Summary: We give a physical derivation of generalized Kähler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of M. Gualtieri [“Generalized complex geometry”, DPhil thesis, Oxford University, (2004)] regarding the equivalence between generalized Kähler geometry and the bi-hermitean geometry of S. J. Gates, C. M. Hull and M. Roček [Nucl. Phys. B 248, 157 (1984)]. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.

Cited in 22 Documents

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
53B35 Local differential geometry of Hermitian and Kählerian structures
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T60 Supersymmetric field theories in quantum mechanics

Keywords:

generalized Kähler geometry; supersymmetric sigma models
Cite Review PDF
Full Text: DOI arXiv

References:

[1] Alekseev A., Strobl T. (2005) Current algebra and differential geometry. JHEP 0503: 035[arXiv:hep-th/0410183] · doi:10.1088/1126-6708/2005/03/035
[2] Alvarez-Gaume L., Freedman D.Z. (1980) Ricci flat Kahler manifolds and supersymmetry. Phys. Lett. B 94, 171 · doi:10.1016/0370-2693(80)90850-3
[3] Bergamin L. (2005) Generalized complex geometry and the Poisson sigma model. Mod. Phys. Lett. A 20, 985 [arXiv:hep-th/0409283] · Zbl 1067.81046 · doi:10.1142/S0217732305017184
[4] Bonechi F., Cattaneo A.S., Zabzine M.: Geometric quantization and non-perturbative Poisson sigma model. [arXiv:math.SG/0507223] (to appear in Adv. Theor. Math. Phys.) · Zbl 1123.53047
[5] Bredthauer A., Lindström U., Persson J.(2006) First-order supersymmetric sigma models and target space geometry. JHEP 0601: 144 [arXiv:hep-th/0508228] · doi:10.1088/1126-6708/2006/01/144
[6] Bonelli G., Zabzine M. (2005) From current algebras for p-branes to topological M-theory. JHEP 0509: 015 [arXiv:hep-th/0507051] · doi:10.1088/1126-6708/2005/09/015
[7] Buscher T., Lindström U., Roček M. (1988) New supersymmetric sigma models with Wess-Zumino terms. Phys. Lett. B 202, 94 · doi:10.1016/0370-2693(88)90859-3
[8] Calvo I.: Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry. [arXiv:hep-th/0511179] · Zbl 1105.53063
[9] Gates S.J., Hull C.M., Roček M.: Twisted multiplets and new supersymmetric nonlinear sigma models. Nucl. Phys. B248, 157 (1984)
[10] Gualtieri M.: Generalized complex geometry. DPhil thesis, Oxford University. [arXiv:math.DG/0401221](2004) · Zbl 1079.53106
[11] Hitchin N. (2003) Generalized Calabi-Yau manifolds. Qt. J. Math. Oxford Ser. 54: 281–308 [arXiv:math.DG/0209099] · Zbl 1076.32019 · doi:10.1093/qmath/hag025
[12] Kapustin A. (2004) Topological strings on noncommutative manifolds. Int. J. Geom. Meth. Mod. Phys. 1, 49 [arXiv:hep-th/0310057] · Zbl 1065.81108 · doi:10.1142/S0219887804000034
[13] Kapustin A., Li Y.: Topological sigma-models with H-flux and twisted generalized complex manifolds. [arXiv:hep-th/0407249] · Zbl 1192.81310
[14] Lindström U.(2004) Generalized N = (2,2) supersymmetric non-linear sigma models. Phys. Lett. B 587, 216 [arXiv:hep-th/0401100] · Zbl 1246.81375 · doi:10.1016/j.physletb.2004.03.014
[15] Lindström U., Minasian R., Tomasiello A., Zabzine M. (2005) Generalized complex manifolds and supersymmetry. Commun. Math. Phys. 257, 235 [arXiv:hep-th/0405085] · Zbl 1118.53048 · doi:10.1007/s00220-004-1265-6
[16] Lindström U., Roček M., von Unge R., Zabzine M.: Generalized Kähler manifolds and off-shell supersymmetry. [arXiv:hep-th/0512164] · Zbl 1114.81077
[17] Witten E.: Mirror manifolds and topological field theory. [arXiv:hep-th/9112056] · Zbl 0904.58009
[18] Zabzine M. (2006) Hamiltonian perspective on generalized complex structure. Commun. Math. Phys. 263, 711 [arXiv:hep-th/0502137] · Zbl 1104.53077 · doi:10.1007/s00220-005-1512-5
[19] Zucchini R. (2004) A sigma model field theoretic realization of Hitchin’s generalized complex geometry. JHEP 0411, 045 [arXiv:hep-th/0409181] · doi:10.1088/1126-6708/2004/11/045
[20] Zumino B. (1979) Supersymmetry and Kähler manifolds. Phys. Lett. B 87, 203 · doi:10.1016/0370-2693(79)90964-X
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.