Hyperkaehler metrics from projective superspace
Lindström, Ulf
Archivum Mathematicum, Tome 043 (2007), p. 491-498 / Harvested from Czech Digital Mathematics Library
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This is a brief review of how sigma models in Projective Superspace have become important tools for constructing new hyperkähler metrics.

Publié le : 2007-01-01
Classification:  51P05,  53C26 
@article{108087,
     author = {Ulf Lindstr\"om},
     title = {Hyperkaehler metrics from projective superspace},
     journal = {Archivum Mathematicum},
     volume = {043},
     year = {2007},
     pages = {491-498},
     zbl = {1199.51024},
     mrnumber = {2381791},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108087}
}

Lindström, Ulf. Hyperkaehler metrics from projective superspace. Archivum Mathematicum, Tome 043 (2007) pp. 491-498. http://gdmltest.u-ga.fr/item/108087/

Alvarez-Gaumé L.; Freedman D. Z. Geometrical structure and ultraviolet finiteness in the supersymmetric sigma model, Comm. Math. Phys. 80, 443 (1981). (1981) | MR 0626710

Arai M.; Kuzenko S. M.; Lindstrom U. Hyperkaehler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace, JHEP 0702, 100 (2007), [arXiv:hep-th/0612174]. | MR 2318051

Buscher T.; Lindstrom U.; Roček M. New supersymmetric sigma models with Wess-Zumino terms, Phys. Lett. B 202, 94 (1988). (1988) | MR 0930852

Galperin A. S.; Ivanov E. A.; Ogievetsky V. I.; Sokatchev E. S. Harmonic Superspace, Cambridge University Press (UK) (2001), 306 p. | MR 1865518 | Zbl 1152.81001

Gates S. J.; Hull C. M.; Roček M. Twisted multiplets and new supersymmetric nonlinear sigma models, Nuclear Phys. B 248, 157 (1984). (1984) | MR 0776369

Gates S. J., Jr.; Kuzenko S. M. The CNM-hypermultiplet nexus, Nuclear Phys. B 543, 122 (1999), [hep-th/9810137]. (1999) | MR 1686128 | Zbl 0958.81179

Gonzalez-Rey F.; Roček M.; Wiles S.; Lindstrom U.; Von Unge R. Feynman rules in $N = 2$ projective superspace. I: Massless hypermultiplets, Nuclear Phys. B 516, 426 (1998), [arXiv:hep-th/9710250]. (1998) | MR 1630237

Gonzalez-Rey F.; Von Unge R. Feynman rules in $N = 2$ projective superspace. II: Massive hypermultiplets, Nuclear Phys. B 516, 449 (1998), [arXiv:hep-th/9711135]. (1998) | MR 1630233 | Zbl 0977.81141

Gonzalez-Rey F. Feynman rules in $N = 2$ projective superspace. III: Yang-Mills multiplet, arXiv:hep-th/9712128.

Grundberg J.; Lindstrom U. Actions for linear multiplets in six-dimensions, Class. Quant. Grav. 2, L33 (1985). (1985) | MR 0786559

Gualtieri M. Generalized complex geometry, Oxford University DPhil thesis, [arXiv:math.DG/0401221]. | MR 2811595 | Zbl 1235.32020

Hitchin N. J.; Karlhede A.; Lindstrom U.; Rocek M. Hyperkahler metrics and supersymmetry, Comm. Math. Phys. 108, 535 (1987). (1987) | MR 0877637

Hitchin N. Generalized Calabi-Yau manifolds, Q. J. Math. 54 (2003), No. 3, 281–308, [arXiv:math.DG/0209099]. | MR 2013140 | Zbl 1076.32019

Ivanov I. T.; Roček M. Supersymmetric sigma models, twistors, and the Atiyah-Hitchin metric, Comm. Math. Phys. 182, 291 (1996), [arXiv:hep-th/9512075]. (1996) | MR 1447294 | Zbl 0882.32014

Karlhede A.; Lindstrom U.; Roček M. Selfinteracting tensor multiplets in $N=2$ superspace, Phys. Lett. B 147, 297 (1984). (1984) | MR 0769049

Karlhede A.; Lindstrom U.; Roček M. Hyperkahler manifolds and nonlinear supermultiplets, Comm. Math. Phys. 108, 529 (1987). (1987) | MR 0877636

Kuzenko S. M. Projective superspace as a double-punctured harmonic superspace, Internat. J. Modern Phys. A 14, 1737 (1999), [arXiv:hep-th/9806147]. (1999) | MR 1686416 | Zbl 0938.81039

Van Nieuwenhuizen P. General theory of coset manifolds and antisymmetric tensors applied to Kaluza-Klein supergravity, Published in Trieste School 1984:0239. (1984)

Kuzenko S. M. Extended supersymmetric nonlinear sigma-models on cotangent bundles of Kähler manifolds: Off-shell realizations, gauging, superpotentials, Talks given at the University of Munich, Imperial College, and Cambridge University (May–June, 2006).

Lindström U.; Ivanov I. T.; Roček M. New $N=4$ superfields and sigma models, Phys. Lett. B 328, 49 (1994). [arXiv:hep-th/9401091]. (1994) | MR 1288922

Lindström U.; Kim B. B.; Roček M. The nonlinear multiplet revisited, Phys. Lett. B 342, 99 (1995) [arXiv:hep-th/9406062]. (1995) | MR 1314388

Lindström U.; Roček M. Scalar tensor duality and $N=1$, $N=2$ nonlinear sigma models, Nuclear Phys. B 222, 285 (1983). (1983) | MR 0710273

Lindström U.; Roček M. New hyperkahler metrics and new supermultiplets, Comm. Math. Phys. 115, 21 (1988). (1988) | MR 0929144

Lindström U.; Roček M. $N=2$ Superyang-Mills theory in projective superspace, Comm. Math. Phys. 128, 191 (1990). (191 ) | MR 1042450

Lindström U.; Roček M.; Von Unge R.; Zabzine M. Generalized Kaehler manifolds and off-shell supersymmetry, arXiv:hep-th/0512164. | Zbl 1114.81077

Lindström U.; Roček M.; Von Unge R.; Zabzine M. Linearizing generalized Kaehler geometry, arXiv:hep-th/0702126.

Zumino B. Supersymmetry and Kahler manifolds, Phys. Lett. B 87, 203 (1979). (1979)