Previous |  Up |  Next

Article

Title: Lectures on generalized complex geometry and supersymmetry (English)
Author: Zabzine, Maxim
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 42
Issue: 5
Year: 2006
Pages: 119-146
Summary lang: English
.
Category: math
.
Summary: These are the lecture notes from the 26th Winter School “Geometry and Physics", Czech Republic, Srní, January 14 – 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry to physics, namely to two-dimensional field theories. We explain in detail the relation between generalized complex geometry and supersymmetry. We briefly review the generalized Kähler and generalized Calabi-Yau manifolds and explain their appearance in physics. (English)
MSC: 53C15
MSC: 53D17
idZBL: Zbl 1164.53342
idMR: MR2322403
.
Date available: 2008-06-06T22:49:14Z
Last updated: 2012-05-10
Stable URL: http://hdl.handle.net/10338.dmlcz/108023
.
Reference: [1] Alekseev A., Strobl T.: Current algebra and differential geometry.JHEP 0503 (2005), 035 [arXiv:hep-th/0410183]. MR 2151966
Reference: [2] Bonechi F., Zabzine M.: .work in progress. Zbl 1201.81097
Reference: [3] Bredthauer A., Lindström U., Persson J., Zabzine M.: Generalized Kaehler geometry from supersymmetric sigma models.Lett. Math. Phys. 77 (2006), 291–308, arXiv:hep-th/0603130. Zbl 1105.53053, MR 2260375
Reference: [4] Calvo I.: Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry.Lett. Math. Phys. 77 (2006), 53–62, arXiv:hep-th/0511179. Zbl 1105.53063, MR 2247462
Reference: [5] A. Cannas da Silva A., Weinstein A.: Geometric models for noncommutative algebras.Berkeley Mathematics Lecture Notes, AMS, Providence, 1999.
Reference: [6] Courant T., Weinstein A.: Beyond Poisson structures.In Action hamiltoniennes de groups. Troisième théorème de Lie (Lyon 1986), volume 27 of Travaux en Cours, 39–49, Hermann, Paris, 1988. MR 0951168
Reference: [7] Courant T.: Dirac manifolds.Trans. Amer. Math. Soc. 319 (1990), 631–661. Zbl 0850.70212, MR 0998124
Reference: [8] Gates S. J., Hull C. M., Roček M.: Twisted multiplets and new supersymmetric nonlinear sigma models.Nucl. Phys. B 248 (1984), 157. MR 0776369
Reference: [9] Graña M.: Flux compactifications in string theory: A comprehensive review.Phys. Rept. 423 (2006), 91 [arXiv:hep-th/0509003]. MR 2193814
Reference: [10] Gualtieri M.: Generalized complex geometry.Oxford University DPhil thesis, arXiv: math.DG/0401221. Zbl 1235.32020
Reference: [11] Hitchin N.: Generalized Calabi-Yau manifolds.Q. J. Math. 54 3 (2003), 281–308 [arXiv:math.DG/0209099]. Zbl 1076.32019, MR 2013140
Reference: [12] Hitchin N.: Instantons, Poisson structures and generalized Kähler geometry.Comm. Math. Phys. 265 (2006), 131–164, arXiv:math.DG/0503432. Zbl 1110.53056, MR 2217300
Reference: [13] Hitchin N.: Brackets, forms and invariant functionals.arXiv:math.DG/0508618. Zbl 1113.53030, MR 2253158
Reference: [14] Kapustin A., Li Y.: Topological sigma-models with H-flux and twisted generalized complex manifolds.arXiv:hep-th/0407249. Zbl 1192.81310, MR 2322555
Reference: [15] Li Y.: On deformations of generalized complex structures: The generalized Calabi-Yau case.arXiv:hep-th/0508030.
Reference: [16] Lindström U.: A brief review of supersymmetric non-linear sigma models and generalized complex geometry.arXiv:hep-th/0603240. Zbl 1164.53400, MR 2322417
Reference: [17] Lindström U., Minasian R., Tomasiello A., Zabzine M.: Generalized complex manifolds and supersymmetry.Comm. Math. Phys. 257 (2005), 235 [arXiv:hep-th/0405085]. Zbl 1118.53048, MR 2163575
Reference: [18] Lindström U., Roček M., von Unge R., Zabzine M.: Generalized Kaehler manifolds and off-shell supersymmetry.Comm. Math. Phys. 269 (2007), 833–849, arXiv:hep-th/0512164. Zbl 1114.81077, MR 2276362
Reference: [19] Liu Z.-J., Weinstein A., Xu P.: Manin triples for Lie bialgebroids.J. Differential Geom. 45 3 (1997), 547–574. Zbl 0885.58030, MR 1472888
Reference: [20] Lyakhovich S., Zabzine M.: Poisson geometry of sigma models with extended supersymmetry.Phys. Lett. B 548 (2002), 243 [arXiv:hep-th/0210043]. Zbl 0999.81044, MR 1948542
Reference: [21] Mackenzie K. C. H.: General theory of Lie groupoids and Lie algebroids.Cambridge University Press, Cambridge, 2005. xxxviii+501 pp. Zbl 1078.58011, MR 2157566
Reference: [22] Pestun V.: Topological strings in generalized complex space.arXiv:hep-th/0603145. Zbl 1154.81024, MR 2322532
Reference: [23] Roytenberg D.: Courant algebroids, derived brackets and even symplectic supermanifolds.(PhD thesis), arXiv:math.DG/9910078. MR 2699145
Reference: [24] Sussmann H.: Orbits of families of vector fields and integrability of distributions.Trans. Amer. Math. Soc. 180 (1973), 171. Zbl 0274.58002, MR 0321133
Reference: [25] Yano K., Kon M.: Structures of manifolds.Series in Pure Mathematics, Vol.3 World Scientific, Singapore, 1984 Yano, K., Differential geometry on complex and almost complex spaces, Pergamon, Oxford, 1965. MR 0794310
Reference: [26] Zabzine M.: Hamiltonian perspective on generalized complex structure.Comm. Math. Phys. 263 (2006), 711 [arXiv:hep-th/0502137]. Zbl 1104.53077, MR 2211820
.

Files

Files Size Format View
ArchMathRetro_042-2006-5_4.pdf 353.5Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo