Hyperkaehler metrics from projective superspace
Archivum mathematicum, Tome 43 (2007) no. 5, pp. 491-498 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

This is a brief review of how sigma models in Projective Superspace have become important tools for constructing new hyperkähler metrics.
This is a brief review of how sigma models in Projective Superspace have become important tools for constructing new hyperkähler metrics.
Classification : 51P05, 53C26
Keywords: superspace; sigma models; hyperkähler geometry
@article{ARM_2007_43_5_a12,
     author = {Lindstr\"om, Ulf},
     title = {Hyperkaehler metrics from projective superspace},
     journal = {Archivum mathematicum},
     pages = {491--498},
     year = {2007},
     volume = {43},
     number = {5},
     mrnumber = {2381791},
     zbl = {1199.51024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a12/}
}
TY  - JOUR
AU  - Lindström, Ulf
TI  - Hyperkaehler metrics from projective superspace
JO  - Archivum mathematicum
PY  - 2007
SP  - 491
EP  - 498
VL  - 43
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a12/
LA  - en
ID  - ARM_2007_43_5_a12
ER  - 
%0 Journal Article
%A Lindström, Ulf
%T Hyperkaehler metrics from projective superspace
%J Archivum mathematicum
%D 2007
%P 491-498
%V 43
%N 5
%U http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a12/
%G en
%F ARM_2007_43_5_a12
Lindström, Ulf. Hyperkaehler metrics from projective superspace. Archivum mathematicum, Tome 43 (2007) no. 5, pp. 491-498. http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a12/

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

[2] 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

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

[4] Galperin A. S., Ivanov E. A., Ogievetsky V. I., Sokatchev E. S.: Harmonic Superspace. Cambridge University Press (UK) (2001), 306 p. | MR | Zbl

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

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

[7] 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]. | MR

[8] 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]. | MR | Zbl

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

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

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

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

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

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

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

[16] Karlhede A., Lindstrom U., Roček M.: Hyperkahler manifolds and nonlinear supermultiplets. Comm. Math. Phys. 108, 529 (1987). | MR

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

[18] van Nieuwenhuizen P.: General theory of coset manifolds and antisymmetric tensors applied to Kaluza-Klein supergravity. Published in Trieste School 1984:0239.

[19] 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).

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

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

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

[23] Lindström U., Roček M.: New hyperkahler metrics and new supermultiplets. Comm. Math. Phys. 115, 21 (1988). | MR

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

[25] Lindström U., Roček M., von Unge R., Zabzine M.: Generalized Kaehler manifolds and off-shell supersymmetry. arXiv:hep-th/0512164. | Zbl

[26] Lindström U., Roček M., von Unge R., Zabzine M.: Linearizing generalized Kaehler geometry. arXiv:hep-th/0702126.

[27] Zumino B.: Supersymmetry and Kahler manifolds. Phys. Lett. B 87, 203 (1979).