Lectures on nonlinear sigma-models in projective superspace

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 44, 2010, Pages

  Kuzenko, Sergei M ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78649674055     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/44/443001     Document Type: Review

References (83)

1. Golfand Yu A and Likhtman E P 1971 Extension of the algebra of Poincaré group generators and violation of P invariance JETP Lett. 13 323
2. Golfand Yu A and Likhtman E P 1971 Pisma Zh. Eksp. Teor. Fiz. 13 452
3. Volkov D V and Akulov V P 1972 Possible universal neutrino interaction JETP Lett. 16 438
4. Volkov D V and Akulov V P 1972 Pisma Zh. Eksp. Teor. Fiz. 16 621
5. Volkov D V and Akulov V P 1973 Is the neutrino a Goldstone particle? Phys. Lett. B 46 109
6. Wess J and Zumino B 1974 Supergauge transformations in four dimensions Nucl. Phys. B 70 39
7. Freedman D Z, van Nieuwenhuizen P and Ferrara S 1976 Progress toward a theory of supergravity Phys. Rev. D 13 3214
8. Deser S and Zumino B 1976 Consistent supergravity Phys. Lett. B 62 335
9. Ferrara S and van Nieuwenhuizen P 1976 Consistent supergravity with complex spin 3/2 gauge fields Phys. Rev. Lett. 37 1669
10. Zumino B 1979 Supersymmetry and Kähler manifolds Phys. Lett. B 87 203
11. Calabi E 1979 Ann. Ecol. Norm. Sup. 12 269
12. Hitchin N J, Karlhede A, Lindström U and Roček M 1987 Hyperkähler metrics and supersymmetry Commun. Math. Phys. 108 535
13. Alvarez-Gaumé L and Freedman D Z 1981 Geometrical structure and ultraviolet finiteness in the supersymmetric sigma model Commun. Math. Phys. 80 443
14. Bagger J and Witten E 1983 Matter couplings in N = 2 supergravity Nucl. Phys. B 222 1
15. Besse A L 2008 Einstein Manifolds (Berlin: Springer)
16. Lindström U and Roček M 1983 Scalar tensor duality and N = 1, 2 nonlinear sigma models Nucl. Phys. B 222 285
17. Karlhede A, Lindström U and Roček M 1984 Self-interacting tensor multiplets in N = 2 superspace Phys. Lett. B 147 297
18. Galperin A, Ivanov E, Ogievetsky V and Sokatchev E 1986 Hyperkähler metrics and harmonic superspace Commun. Math. Phys. 103 515
19. Galperin A, Ivanov E, Kalitsyn S, Ogievetsky V and Sokatchev E 1984 Unconstrained N = 2 matter, Yang-Mills and supergravity theories in harmonic superspace Class. Quantum Grav. 1 469
20. Galperin A S, Ivanov E A, Ogievetsky V I and Sokatchev E S 2001 Harmonic Superspace (Cambridge: Cambridge University Press)
21. Gates S J Jr, Hull C M and Roček M 1984 Twisted multiplets and new supersymmetric nonlinear sigma models Nucl. Phys. B 248 157
22. Lindström U and Roček M 1988 New hyperkähler metrics and new supermultiplets Commun. Math. Phys. 115 21
23. Lindström U and Roček M 1990 N = 2 super Yang-Mills theory in projective superspace Commun. Math. Phys. 128 191
24. Gonzalez-Rey F, Roček M, Wiles S, Lindström U and von Unge R 1998 Feynman rules in N = 2 projective superspace: I. Massless hypermultiplets Nucl. Phys. B 516 426 (arXiv:hep-th/9710250)
25. Kuzenko S M 1999 Projective superspace as a double-punctured harmonic superspace Int. J. Mod. Phys. A 14 1737 (arXiv:hep-th/9806147)
26. Jain D and Siegel W 2009 Deriving projective hyperspace from harmonic Phys. Rev. D 80 045024 (arXiv:0903.3588 [hep-th])
27. Swann A 1991 HyperKähler and quaternion Kähler geometry Math. Ann. 289 421
28. Galicki K 1992 Geometry of the scalar couplings in N = 2 supergravity models Class. Quantum Grav. 9 27
29. Boyer C P and Galicki K 2008 Sasakian Geometry (Oxford: Oxford University Press)
30. de Wit B, Roček M and Vandoren S 2001 Hypermultiplets, hyperkähler cones and quaternion-Kähler geometry J. High Energy Phys. JHEP 02 (2001) 039 (arXiv:hep-th/0101161)
31. Sezgin E and Tanii Y 1995 Superconformal sigma models in higher than two dimensions Nucl. Phys. B 443 70 (arXiv:hep-th/9412163)
32. Wess J and Bagger J 1992 Supersymmetry and Supergravity (Princeton, NJ: Princeton University Press)
33. Buchbinder I L and Kuzenko S M 1998 Ideas and Methods of Supersymmetry and Supergravity or a Walk through Superspace (Bristol: IOP)
34. Akulov V P and Volkov D V 1974 Goldstone fields with spin 1/2 Theor. Math. Phys. 18 28
35. Akulov V P and Volkov D V 1974 Teor. Mat. Fiz. 18 39
36. Haag R, Lopuszanski J T and Sohnius M 1975 All possible generators of supersymmetries of the S-matrix Nucl. Phys. B 88 257
37. Gates S J Jr, Grisaru M T, Roček M and Siegel W 1983 Superspace, or one thousand and one lessons in supersymmetry Front. Phys. 58 1 (arXiv:hep-th/0108200)
38. Kirillov A A 1976 Elements of the Theory of Representations (Berlin: Springer)
39. Salam A and Strathdee J A 1974 Super-gauge transformations Nucl. Phys. B 76 477
40. Berezin F A 1966 The Method of Second Quantization (New York: Academic)
41. Hull C M, Karlhede A, Lindström U and Roček M 1986 Nonlinear sigma models and their gauging in and out of superspace Nucl. Phys. B 266 1
42. Kuzenko S M 2010 N = 2 supersymmetric sigma-models and duality J. High Energy Phys. JHEP 01 (2010) 115 (arXiv:0910.5771 [hep-th])
43. Rosly A A 1983 Super Yang-Mills constraints as integrability conditions Proc. Int. Seminar on Group Theoretical Methods in Physics (Zvenigorod, USSR, 1982) vol 1 ed M A Markov (Moscow: Nauka) p 263 (in Russian)
44. Witten E 1978 An interpretation of classical Yang-Mills theory Phys. Lett. B 77 394
45. Rosly A A and Schwarz A S 1986 Supersymmetry in a space with auxiliary dimensions Commun. Math. Phys. 105 645
46. Želobenko D P 1978 Compact Lie Groups and Their Representations (Providence, RI: American Mathematical Society)
47. Siegel W 1985 Chiral actions for N = 2 supersymmetric tensor multiplets Phys. Lett. B 153 51
48. Whittaker E T 1903 On the partial differential equations of mathematical physics Math. Ann. 57 333
49. Whittaker E T and Watson G N 1927 A Course of Modern Analysis 4th edn (Cambridge: Cambridge University Press)
50. Ketov S V, Lokhvitsky B B and Tyutin I V 1987 Hyperkähler sigma models in extended superspace Theor. Math. Phys. 71 496
51. Ketov S V, Lokhvitsky B B and Tyutin I V 1987 Teor. Mat. Fiz. 71 226
52. Wess J 1975 Supersymmetry and internal symmetry Acta Phys. Austriaca 41 409
53. Zumino B 1980 Superspace Unification of the Fundamental Particle Interactions ed S Ferrara, J Ellis and P van Nieuwenhuizen (New York: Plenum) p 101
54. Gates S J Jr and Siegel W 1980 Understanding constraints in superspace formulations of supergravity Nucl. Phys. B 163 519
55. Gates S J Jr and Siegel W 1981 Variant superfield representations Nucl. Phys. B 187 389
56. Siegel W 1979 Gauge spinor superfield as a scalar multiplet Phys. Lett. B 85 333
57. Gates S J Jr and Kuzenko S M 1999 The CNM-hypermultiplet nexus Nucl. Phys. B 543 122 (arXiv:hep-th/9810137)
58. Lindström U and Roček M 2010 Properties of hyperkähler manifolds and their twistor spaces Commun. Math. Phys. 293 257 (arXiv:0807.1366 [hep-th])
59. Gates S J Jr and Kuzenko S M 2000 4D N = 2 supersymmetric off-shell sigma models on the cotangent bundles of Kähler manifolds Fortsch. Phys. 48 115 (arXiv:hep-th/9903013)
60. Kuzenko S M and Linch W D 2006 On five-dimensional superspaces J. High Energy Phys. JHEP 02 (2006) 038 (arXiv:hep-th/0507176)
61. Kuzenko S M 2007 On superconformal projective hypermultiplets J. High Energy Phys. JHEP 12 (2007) 010 (arXiv:0710.1479 [hep-th])
62. Kaledin D 1999 Hyperkähler structureson total spacesofholomorphic cotangent bundles Hyperkähler Manifolds ed D Kaledin and M Verbitsky (Cambridge, MA: International Press) (arXiv:alg-geom/9710026)
63. Kaledin D 2001 A canonical hyperkähler metric on the total space of a cotangent bundle Quaternionic Structures in Mathematics and Physics ed S Marchiafava, P Piccinni and M Pontecorvo (Singapore: World Scientific) (arXiv:alg-geom/0011256)
64. Feix B 1999 Hyperkähler metrics on cotangent bundles Cambridge PhD thesis
65. Feix B 2001 Hyperkähler metrics on cotangent bundles J. Reine Angew. Math. 532 33
66. Arai M and Nitta M 2006 Hyper-Kähler sigma models on (co) tangent bundles with SO (n) isometry Nucl. Phys. B 745 208 (arXiv:hep-th/0602277)
67. Arai M, Kuzenko S M and Lindström U 2007 Hyperkähler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace J. High Energy Phys. JHEP 02 (2007) 100 (arXiv:hep-th/0612174)
68. Arai M, Kuzenko SM and Lindström U 2007 Polar supermultiplets, Hermitian symmetric spaces and hyperkähler metrics J. High Energy Phys. JHEP 12 (2007) 008 (arXiv:0709.2633 [hep-th])
69. Kuzenko S M and Novak J 2008 Chiral formulation for hyperkähler sigma-models on cotangent bundles of symmetric spaces J. High Energy Phys. JHEP 12 (2008) 072 (arXiv:0811.0218 [hep-th])
70. Bochner S 1947 Curvature in Hermitian metric Bull. Am. Math. Soc. 53 179
71. Calabi E 1953 Isometric imbedding of complex manifolds Ann. Math. 58 1
72. Calabi E 1960 On compact, locally symmetric Kähler manifolds Ann. Math. 71 472
73. Farkas H M and Kra I 1992 Riemann Surfaces (Berlin: Springer)
74. Biquard O and Gauduchon P 1997 Hyperkähler metrics on cotangent bundles of Hermitian symmetric spaces Geometry and Physics (Lect. Notes Pure Appl. Math. vol 184) ed J Andersen, J Dupont, H Petersen and A Swann (New York: Dekker) p 287
75. Berkovits N and Siegel W 1996 Superspace effective actions for 4D compactifications of heterotic and type II superstrings Nucl. Phys. B 462 213 (arXiv:hep-th/9510106)
76. Kuzenko S M, Lindström U and von Unge R 2009 New extended superconformal sigma models and quaternion Kähler manifolds J. High Energy Phys. JHEP 09 (2009) 119 (arXiv:0906.4393 [hep-th])
77. Grundberg J and Lindström U 1985 Actions for linear multiplets in six dimensions Class. Quantum Grav. 2 L33
78. Gates S J Jr, Penati S and Tartaglino-Mazzucchelli G 2006 6D supersymmetric nonlinear sigma-models in 4D, N = 1 superspace J. High Energy Phys. JHEP 09 (2006) 006 (arXiv:hep-th/0604042)
79. Kuzenko S M 2006 On compactified harmonic/projective superspace, 5D superconformal theories, and all that Nucl. Phys. B 745 176 (arXiv:hep-th/ 0601177)
80. Kuzenko S M, Lindström U, Roček M and Tartaglino-Mazzucchelli G 2008 4DN= 2 supergravity and projective superspace J. High Energy Phys. JHEP 09 (2008) 051 (arXiv:0805.4683)
81. Kuzenko S M, Lindström U, Roček M and Tartaglino-Mazzucchelli G 2009 On conformal supergravity and projective superspace J. High Energy Phys. JHEP 08 (2009) 023 (arXiv:0905.0063 [hep-th])
82. Berezin F A 1987 Introduction to Superanalysis (Dordrecht: Kluwer)
83. Higashijima K, Itou E and Nitta M 2002 Normal coordinates in Kähler manifolds and the background field method Prog. Theor. Phys. 108 185 (arXiv:hep-th/0203081)