SO and USp Kähler and hyper-Kähler quotients and lumps

Nuclear Physics B

Volumn 815, Issue 3, 2009, Pages 495-538

  Eto, Minoru ^a,b   Fujimori, Toshiaki ^c   Gudnason, Sven Bjarke ^a,b   Nitta, Muneto ^d   Ohashi, Keisuke ^e  

^a UNIVERSITY OF PISA   (Italy)

^b INFN SEZIONE DI PISA   (Italy)

^c TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^d KEIO UNIVERSITY   (Japan)

^e UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 64449083864     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2009.01.019     Document Type: Article

References (143)

1. Zumino B. Supersymmetry and Kahler manifolds. Phys. Lett. B 87 (1979) 203
2. Alvarez-Gaume L., and Freedman D.Z. Geometrical structure and ultraviolet finiteness in the supersymmetric sigma model. Commun. Math. Phys. 80 (1981) 443
3. Curtright T.L., and Freedman D.Z. Nonlinear sigma models with extended supersymmetry in four dimensions. Phys. Lett. B 90 (1980) 71
4. Curtright T.L., and Freedman D.Z. Phys. Lett. B 91 (1980) 487 Erratum
5. Alvarez-Gaume L., and Freedman D.Z. Ricci-flat Kahler manifolds and supersymmetry. Phys. Lett. B 94 (1980) 171
6. Roček M., and Townsend P.K. Three loop finiteness of the N = 4 supersymmetric nonlinear sigma model. Phys. Lett. B 96 (1980) 72
7. Lindström U., and Roček M. Scalar-tensor duality and N = 1, N = 2 nonlinear sigma models. Nucl. Phys. B 222 (1983) 285
8. Hitchin N.J., Karlhede A., Lindström U., and Roček M. Hyper-Kahler metrics and supersymmetry. Commun. Math. Phys. 108 (1987) 535
9. Antoniadis I., and Pioline B. Higgs branch, hyper-Kaehler quotient and duality in SUSY N = 2 Yang-Mills theories. Int. J. Mod. Phys. A 12 (1997) 4907. hep-th/9607058
10. Argyres P.C., Plesser M.R., and Seiberg N. The moduli space of N = 2 SUSY QCD and duality in N = 1 SUSY QCD. Nucl. Phys. B 471 (1996) 159. hep-th/9603042
11. Grisaru M.T., Riva F., and Zanon D. The one loop effective potential in superspace. Nucl. Phys. B 214 (1983) 465
12. Grisaru M.T., Rocek M., and von Unge R. Effective Kähler potentials. Phys. Lett. B 383 (1996) 415. hep-th/9605149
13. Clark T.E., and Love S.T. The Wilson effective Kaehler potential for supersymmetric nonlinear sigma models. Phys. Rev. D 56 (1997) 2461. hep-th/9701134
14. Brignole A. One-loop Kaehler potential in non-renormalizable theories. Nucl. Phys. B 579 (2000) 101. hep-th/0001121
15. Nibbelink S.G., and Nyawelo T.S. Two loop effective Kaehler potential of (non-)renormalizable supersymmetric models. JHEP 0601 (2006) 034. hep-th/0511004
16. Banin A.T., Buchbinder I.L., and Pletnev N.G. On quantum properties of the four-dimensional generic chiral superfield model. Phys. Rev. D 74 (2006) 045010. hep-th/0606242
17. Calabi E. Métriques kählériennes et fibrés holomorphes. Ann. Sci. Ec. Norm. Sup. 12 (1979) 269
18. Atiyah M.F., Hitchin N.J., Drinfeld V.G., and Manin Yu.I. Construction of instantons. Phys. Lett. A 65 (1978) 185
19. Christ N.H., Weinberg E.J., and Stanton N.K. General self-dual Yang-Mills solutions. Phys. Rev. D 18 (1978) 2013
20. Corrigan E., Fairlie D.B., Templeton S., and Goddard P. A Green's function for the general selfdual gauge field. Nucl. Phys. B 140 (1978) 31
21. Dorey N., Hollowood T.J., Khoze V.V., Mattis M.P., and Vandoren S. Multi-instanton calculus and the AdS/CFT correspondence in N = 4. Nucl. Phys. B 552 (1999) 88. hep-th/9901128
22. Atiyah M.F., and Hitchin N.J. Low-energy scattering of non-Abelian monopoles. Phys. Lett. A 107 (1985) 21
23. Atiyah M.F., and Hitchin N.J. Low-energy scattering of non-Abelian magnetic monopoles. Philos. Trans. R. Soc. London A 315 (1985) 459
24. Gibbons G.W., Goto R., and Rychenkova P. Hyper-Kaehler quotient construction of BPS monopole moduli spaces. Commun. Math. Phys. 186 (1997) 585. hep-th/9608085
25. Kronheimer P.B. The construction of ALE spaces as hyper-Kahler quotients. J. Diff. Geom. 29 (1989) 665
26. Lindström U., Roček M., and von Unge R. Hyper-Kaehler quotients and algebraic curves. JHEP 0001 (2000) 022. hep-th/9908082
27. Kronheimer P.B., and Nakajima H. Yang-Mills instantons on ALE gravitational instantons. Math. Ann. 288 (1990) 263
28. Nakajima H. Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras. Duke Math. J. 76 (1994) 365
29. Bielawski R. Complete hyper-Kaehler 4n-manifolds with n commuting tri-Hamiltonian vector fields. Math. Ann. 314 (1999) 505. math.dg/9808134
30. Seiberg N., and Witten E. Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD. Nucl. Phys. B 431 (1994) 484. hep-th/9408099
31. Argyres P.C., Plesser M.R., and Shapere A.D. N = 2 moduli spaces and N = 1 dualities for SO (n (c)) and USp (2 n (c)) super-QCD. Nucl. Phys. B 483 (1997) 172. hep-th/9608129
32. Eto M., Isozumi Y., Nitta M., Ohashi K., Ohta K., Sakai N., and Tachikawa Y. Global structure of moduli space for BPS walls. Phys. Rev. D 71 (2005) 105009. hep-th/0503033
33. Luty M.A., and Taylor W. Varieties of vacua in classical supersymmetric gauge theories. Phys. Rev. D 53 (1996) 3399. hep-th/9506098
34. Intriligator K.A., and Seiberg N. Lectures on supersymmetric gauge theories and electric-magnetic duality. Nucl. Phys. B (Proc. Suppl.) 45BC (1996) 1. hep-th/9509066
35. Intriligator K.A., and Seiberg N. Duality, monopoles, dyons, confinement and oblique confinement in supersymmetric SO (N (c)) gauge theories. Nucl. Phys. B 444 (1995) 125. hep-th/9503179
36. Intriligator K.A., and Pouliot P. Exact superpotentials, quantum vacua and duality in supersymmetric SP (N (c)) gauge theories. Phys. Lett. B 353 (1995) 471. hep-th/9505006
37. Gray J., Hanany A., He Y.H., Jejjala V., and Mekareeya N. SQCD: A geometric apercu. JHEP 0805 (2008) 099. arXiv:0803.4257 [hep-th]
38. Hanany A., and Mekareeya N. Counting gauge invariant operators in SQCD with classical gauge groups. arXiv:0805.3728 [hep-th]
39. Polyakov A.M., and Belavin A.A. Metastable states of two-dimensional isotropic ferromagnets. JETP Lett. 22 (1975) 245
40. Polyakov A.M., and Belavin A.A. Metastable states of two-dimensional isotropic ferromagnets. Pis'ma Zh. Eksp. Teor. Fiz. 22 (1975) 503
41. Golo V.L., and Perelomov A.M. Solution of the duality equations for the two-dimensional SU (N) invariant chiral model. Phys. Lett. B 79 (1978) 112
42. D'Adda A., Luscher M., and Di Vecchia P. A 1 / N expandable series of nonlinear sigma models with instantons. Nucl. Phys. B 146 (1978) 63
43. (N - 1) model. Nucl. Phys. B 174 (1980) 397
44. Macfarlane A.J. Generalizations of sigma models and Cp (N) models and instantons. Phys. Lett. B 82 (1979) 239
45. Din A.M., and Zakrzewski W.J. Classical solutions in Grassmannian sigma models. Lett. Math. Phys. 5 (1981) 553
46. Din A.M., and Zakrzewski W.J. Further properties of classical solutions in Grassmannian sigma models. Nucl. Phys. B 237 (1984) 461
47. Perelomov A.M. Chiral models: Geometrical aspects. Phys. Rep. 146 (1987) 135
48. Morozov A.Y., Perelomov A.M., and Shifman M.A. Exact Gell-Mann-Low function of supersymmetric Kahler sigma models. Nucl. Phys. B 248 (1984) 279
49. Naganuma M., Nitta M., and Sakai N. BPS lumps and their intersections in N = 2 SUSY nonlinear sigma models. Gravit. Cosmol. 8 (2002) 129. hep-th/0108133
50. Portugues R., and Townsend P.K. Sigma-model soliton intersections from exceptional calibrations. JHEP 0204 (2002) 039. hep-th/0203181
51. Eto M., Isozumi Y., Nitta M., and Ohashi K. 1/2, 1/4 and 1/8 BPS equations in SUSY Yang-Mills-Higgs systems: Field theoretical brane configurations. Nucl. Phys. B 752 (2006) 140. hep-th/0506257
52. 1 model in (2 + 1) dimensions. Phys. Lett. B 158 (1985) 424
53. 1 model. Nucl. Phys. B 344 (1990) 33
54. Vachaspati T., and Achucarro A. Semilocal cosmic strings. Phys. Rev. D 44 (1991) 3067
55. Achucarro A., and Vachaspati T. Semilocal and electroweak strings. Phys. Rep. 327 (2000) 347. hep-ph/9904229
56. Hindmarsh M. Existence and stability of semilocal strings. Phys. Rev. Lett. 68 (1992) 1263
57. Hindmarsh M. Semilocal topological defects. Nucl. Phys. B 392 (1993) 461. hep-ph/9206229
58. Preskill J. Semilocal defects. Phys. Rev. D 46 (1992) 4218. hep-ph/9206216
59. Abrikosov A.A. On the magnetic properties of superconductors of the second group. Sov. Phys. JETP 5 (1957) 1174
60. Abrikosov A.A. On the magnetic properties of superconductors of the second group. Zh. Eksp. Teor. Fiz. 32 (1957) 1442
61. Nielsen H.B., and Olesen P. Vortex-line models for dual strings. Nucl. Phys. B 61 (1973) 45
62. Benson K., and Bucher M. Skyrmions and semilocal strings in cosmology. Nucl. Phys. B 406 (1993) 355. hep-ph/9304214
63. Achucarro A., Borrill J., and Liddle A.R. The formation rate of semilocal strings. Phys. Rev. Lett. 82 (1999) 3742. hep-ph/9802306
64. Achucarro A., Salmi P., and Urrestilla J. Semilocal cosmic string networks. Phys. Rev. D 75 (2007) 121703. astro-ph/0512487
65. Laguna P., Natchu V., Matzner R.A., and Vachaspati T. Intercommutation of semilocal strings and skyrmions. Phys. Rev. Lett. 98 (2007) 041602. hep-th/0604177
66. Urrestilla J., Bevis N., Hindmarsh M., Kunz M., and Liddle A.R. Cosmic microwave anisotropies from BPS semilocal strings. JCAP 0807 (2008) 010. arXiv:0711.1842 [astro-ph]
67. Battye R.A., Garbrecht B., and Pilaftsis A. Textures and semi-local strings in SUSY hybrid inflation. arXiv:0807.1729 [hep-ph]
68. Dasgupta K., Hsu J.P., Kallosh R., Linde A., and Zagermann M. D3/D7 brane inflation and semilocal strings. JHEP 0408 (2004) 030. hep-th/0405247
69. Dasgupta K., Firouzjahi H., and Gwyn R. Lumps in the throat. JHEP 0704 (2007) 093. hep-th/0702193
70. Dasgupta K., Hussin V., and Wissanji A. Quaternionic Kahler manifolds, constrained instantons and the magic square: I. Nucl. Phys. B 793 (2008) 34. arXiv:0708.1023 [hep-th]
71. Hanany A., and Tong D. Vortices, instantons and branes. JHEP 0307 (2003) 037. hep-th/0306150
72. Auzzi R., Bolognesi S., Evslin J., Konishi K., and Yung A. Nonabelian superconductors: Vortices and confinement in N = 2 SQCD. Nucl. Phys. B 673 (2003) 187. hep-th/0307287
73. Eto M., Isozumi Y., Nitta M., Ohashi K., and Sakai N. Moduli space of non-Abelian vortices. Phys. Rev. Lett. 96 (2006) 161601. hep-th/0511088
74. Eto M., Konishi K., Marmorini G., Nitta M., Ohashi K., Vinci W., and Yokoi N. Non-Abelian vortices of higher winding numbers. Phys. Rev. D 74 (2006) 065021. hep-th/0607070
75. Isozumi Y., Nitta M., Ohashi K., and Sakai N. All exact solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield equation. Phys. Rev. D 71 (2005) 065018. hep-th/0405129
76. Isozumi Y., Nitta M., Ohashi K., and Sakai N. Construction of non-Abelian walls and their complete moduli space. Phys. Rev. Lett. 93 (2004) 161601. hep-th/0404198
77. Isozumi Y., Nitta M., Ohashi K., and Sakai N. Non-Abelian walls in supersymmetric gauge theories. Phys. Rev. D 70 (2004) 125014. hep-th/0405194
78. Eto M., Isozumi Y., Nitta M., Ohashi K., and Sakai N. Solitons in the Higgs phase: The moduli matrix approach. J. Phys. A 39 (2006) R315. hep-th/0602170
79. Eto M., Isozumi Y., Nitta M., Ohashi K., and Sakai N. Solitons in supersymmetric gauge theories: Moduli matrix approach. Proceedings of 7th Workshop on Continuous Advances in QCD. Minneapolis, Minnesota, 11-14 May 2006. Minneapolis 2006, Continuous Advances in QCD (2006) 58-71. hep-th/0607225
80. Hashimoto K., and Tong D. Reconnection of non-Abelian cosmic strings. JCAP 0509 (2005) 004. hep-th/0506022
81. Auzzi R., Shifman M., and Yung A. Composite non-Abelian flux tubes in N = 2 SQCD. Phys. Rev. D 73 (2006) 105012. hep-th/0511150
82. Auzzi R., Shifman M., and Yung A. Phys. Rev. D 76 (2007) 109901 Erratum
83. Eto M., Hashimoto K., Marmorini G., Nitta M., Ohashi K., and Vinci W. Universal reconnection of non-Abelian cosmic strings. Phys. Rev. Lett. 98 (2007) 091602. hep-th/0609214
84. Eto M., Isozumi Y., Nitta M., Ohashi K., and Sakai N. Manifestly supersymmetric effective Lagrangians on BPS solitons. Phys. Rev. D 73 (2006) 125008. hep-th/0602289
85. Tong D. TASI lectures on solitons. hep-th/0509216
86. Konishi K. The magnetic monopoles seventy-five years later. Lect. Notes Phys. 737 (2008) 471. hep-th/0702102
87. Shifman M., and Yung A. Supersymmetric solitons and how they help us understand non-Abelian gauge theories. Rev. Mod. Phys. 79 (2007) 1139. hep-th/0703267
88. Tong D. Monopoles in the Higgs phase. Phys. Rev. D 69 (2004) 065003. hep-th/0307302
89. Shifman M., and Yung A. Non-Abelian string junctions as confined monopoles. Phys. Rev. D 70 (2004) 045004. hep-th/0403149
90. Hanany A., and Tong D. Vortex strings and four-dimensional gauge dynamics. JHEP 0404 (2004) 066. hep-th/0403158
91. Eto M., Isozumi Y., Nitta M., Ohashi K., and Sakai N. Instantons in the Higgs phase. Phys. Rev. D 72 (2005) 025011. hep-th/0412048
92. Fujimori T., Nitta M., Ohta K., Sakai N., and Yamazaki M. Intersecting solitons, amoeba and tropical geometry. Phys. Rev. D 78 (2008) 105004. arXiv:0805.1194 [hep-th]
93. Auzzi R., Bolognesi S., Evslin J., and Konishi K. Non-Abelian monopoles and the vortices that confine them. Nucl. Phys. B 686 (2004) 119. hep-th/0312233
94. Auzzi R., Bolognesi S., Evslin J., Konishi K., and Murayama H. Non-Abelian monopoles. Nucl. Phys. B 701 (2004) 207. hep-th/0405070
95. Eto M., et al. Non-Abelian duality from vortex moduli: A dual model of color-confinement. Nucl. Phys. B 780 (2007) 161. hep-th/0611313
96. Dorigoni D., Konishi K., and Ohashi K. Non-Abelian vortices without dynamical abelianization. arXiv:0801.3284 [hep-th]
97. Shifman M., and Yung A. Non-Abelian flux tubes in SQCD: Supersizing world-sheet supersymmetry. Phys. Rev. D 72 (2005) 085017. hep-th/0501211
98. Gorsky A., Shifman M., and Yung A. N = 1 supersymmetric quantum chromodynamics: How confined non-Abelian monopoles emerge from quark condensation. Phys. Rev. D 75 (2007) 065032. hep-th/0701040
99. Edalati M., and Tong D. Heterotic vortex strings. JHEP 0705 (2007) 005. hep-th/0703045
100. Tong D. The quantum dynamics of heterotic vortex strings. JHEP 0709 (2007) 022. hep-th/0703235
101. Shifman M., and Yung A. Heterotic flux tubes in N = 2 SQCD with N = 1 preserving deformations. Phys. Rev. D 77 (2008) 125016. arXiv:0803.0158 [hep-th]
102. Shifman M., and Yung A. Large-N solution of the heterotic N = (0, 2) two-dimensional CP (N - 1) model. Phys. Rev. D 77 (2008) 125017. arXiv:0803.0698 [hep-th]
103. Collie B. Dyonic non-Abelian vortices. arXiv:0809.0394 [hep-th]
104. Shifman M., and Yung A. Non-Abelian semilocal strings in N = 2 supersymmetric QCD. Phys. Rev. D 73 (2006) 125012. hep-th/0603134
105. Eto M., et al. On the moduli space of semilocal strings and lumps. Phys. Rev. D 76 (2007) 105002. arXiv:0704.2218 [hep-th]
106. Ferretti L., Gudnason S.B., and Konishi K. Non-Abelian vortices and monopoles in SO (N) theories. Nucl. Phys. B 789 (2008) 84. arXiv:0706.3854 [hep-th]
107. Eto M., Fujimori T., Gudnason S.B., Konishi K., Nitta M., Ohashi K., and Vinci W. Constructing non-Abelian vortices with arbitrary gauge groups. arXiv:0802.1020 [hep-th] Phys. Lett. B, in press
108. Fayet P., and Iliopoulos J. Phys. Lett. B 51 (1974) 461
109. Aoyama S. The supersymmetric U (N, R) sigma model and its 0 (2) extended supersymmetry. Nuovo Cimento A 57 (1980) 176
110. Higashijima K., and Nitta M. Supersymmetric nonlinear sigma models as gauge theories. Prog. Theor. Phys. 103 (2000) 635. hep-th/9911139
111. Gates S.J., and Kuzenko S.M. The CNM-hypermultiplet nexus. Nucl. Phys. B 543 (1999) 122. hep-th/9810137
112. Gates S.J., and Kuzenko S.M. 4D N = 2 supersymmetric off-shell sigma models on the cotangent bundles of Kaehler manifolds. Fortschr. Phys. 48 (2000) 115. hep-th/9903013
113. Gates S.J., Hubsch T., and Kuzenko S.M. CNM models, holomorphic functions and projective superspace C-maps. Nucl. Phys. B 557 (1999) 443. hep-th/9902211
114. Arai M., and Nitta M. Hyper-Kaehler sigma models on (co)tangent bundles with SO (n) isometry. Nucl. Phys. B 745 (2006) 208. hep-th/0602277
115. Arai M., Kuzenko S.M., and Lindstrom U. Hyperkaehler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace. JHEP 0702 (2007) 100. hep-th/0612174
116. Arai M., Kuzenko S.M., and Lindstrom U. Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics. JHEP 0712 (2007) 008. arXiv:0709.2633 [hep-th]
117. Arai M., Nitta M., and Sakai N. Vacua of massive hyper-Kaehler sigma models of non-Abelian quotient. Prog. Theor. Phys. 113 (2005) 657. hep-th/0307274
118. Arai M., Nitta M., and Sakai N. Massive hyper-Kaehler sigma models and BPS domain walls. Phys. At. Nucl. 68 (2005) 1634
119. Arai M., Nitta M., and Sakai N. Massive hyper-Kaehler sigma models and BPS domain walls. Yad. Fiz. 68 (2005) 1698. hep-th/0401102
120. Bando M., Kuramoto T., Maskawa T., and Uehara S. Structure of nonlinear realization in supersymmetric theories. Phys. Lett. B 138 (1984) 94
121. Bando M., Kuramoto T., Maskawa T., and Uehara S. Nonlinear realization in supersymmetric theories. Prog. Theor. Phys. 72 (1984) 313
122. Bando M., Kuramoto T., Maskawa T., and Uehara S. Nonlinear realization in supersymmetric theories. 2. Prog. Theor. Phys. 72 (1984) 1207
123. Higashijima K., Nitta M., Ohta K., and Ohta N. Low energy theorems in N = 1 supersymmetric theory. Prog. Theor. Phys. 98 (1997) 1165. hep-th/9706219
124. Kotcheff A.C.W., and Shore G.M. Kahler sigma models from supersymmetric gauge theories. Int. J. Mod. Phys. A 4 (1989) 4391
125. Nitta M. Moduli space of global symmetry in N = 1 supersymmetric theories and the quasi-Nambu-Goldstone bosons. Int. J. Mod. Phys. A 14 (1999) 2397. hep-th/9805038
126. Eto M., Fujimori T., Nitta M., Ohashi K., and Sakai N. Domain walls with non-Abelian clouds. Phys. Rev. D 77 (2008) 125008. arXiv:0802.3135 [hep-th]
127. Eto M., Nitta M., and Sakai N. Effective theory on non-Abelian vortices in six dimensions. Nucl. Phys. B 701 (2004) 247. hep-th/0405161
128. Benson K.M., Manohar A.V., and Saadi M. QCD flux tubes as sigma model relics. Phys. Rev. Lett. 74 (1995) 1932. hep-th/9409042
129. Benson K.M., and Saadi M. QCD flux tubes in a current algebra approach. Phys. Rev. D 51 (1995) 3096. hep-th/9409109
130. Dancer A., and Swann A. Hyperkähler metrics of cohomogeneity one. J. Geom. Phys. 21 (1997) 218
131. Higashijima K., Kimura T., and Nitta M. Ricci-flat Kaehler manifolds from supersymmetric gauge theories. Nucl. Phys. B 623 (2002) 133. hep-th/0108084
132. Higashijima K., Kimura T., and Nitta M. Gauge theoretical construction of non-compact Calabi-Yau manifolds. Ann. Phys. 296 (2002) 347. hep-th/0110216
133. Higashijima K., Kimura T., and Nitta M. Calabi-Yau manifolds of cohomogeneity one as complex line bundles. Nucl. Phys. B 645 (2002) 438. hep-th/0202064
134. Alvarez-Gaume L., and Freedman D.Z. Potentials for the supersymmetric nonlinear sigma model. Commun. Math. Phys. 91 (1983) 87
135. Gates S.J. Superspace formulation of new nonlinear sigma models. Nucl. Phys. B 238 (1984) 349
136. Gauntlett J.P., Tong D., and Townsend P.K. Multi-domain walls in massive supersymmetric sigma-models. Phys. Rev. D 64 (2001) 025010. hep-th/0012178
137. Arai M., Naganuma M., Nitta M., and Sakai N. Manifest supersymmetry for BPS walls in N = 2 nonlinear sigma models. Nucl. Phys. B 652 (2003) 35. hep-th/0211103
138. Arai M., Naganuma M., Nitta M., and Sakai N. BPS wall in N = 2 SUSY nonlinear sigma model with Eguchi-Hanson manifold. In: Arafune J., et al. (Ed). Garden of Quanta - In honor of Hiroshi Ezawa (2003), World Scientific, Singapore 299-325. hep-th/0302028
139. Gauntlett J.P., Tong D., and Townsend P.K. Supersymmetric intersecting domain walls in massive hyper-Kaehler sigma models. Phys. Rev. D 63 (2001) 085001. hep-th/0007124
140. Leese R.A. Q lumps and their interactions. Nucl. Phys. B 366 (1991) 283
141. Abraham E. Nonlinear sigma models and their Q lump solutions. Phys. Lett. B 278 (1992) 291
142. Bak D., Hahn S.O., Lee J., and Oh P. Supersymmetric Q-lumps in the Grassmannian nonlinear sigma models. Phys. Rev. D 75 (2007) 025004. hep-th/0610067
143. Nakajima H., Oh P., and Shin S. Quantum SUSY algebra of Q-lump in the massive Grassmannian sigma model. arXiv:0808.1019 [hep-th]