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Generalized Kähler manifolds and off-shell supersymmetry. (English) Zbl 1114.81077
Summary: We solve the long standing problem of finding an off-shell supersymmetric formulation for a general \(N = (2, 2)\) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kähler potential for any generalized Kähler manifold; this potential is the superspace Lagrangian.

81T60 Supersymmetric field theories in quantum mechanics
53C55 Global differential geometry of Hermitian and Kählerian manifolds
32Q15 Kähler manifolds
81T10 Model quantum field theories
81R12 Groups and algebras in quantum theory and relations with integrable systems
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[1] Gates S.J., Hull C.M., Roček M. (1984) Twisted multiplets and new supersymmetric nonlinear sigma models. Nucl. Phys. B248, 157
[2] Buscher T., Lindström U., Roček M. (1988) New supersymmetric sigma models with wess-zumino terms. Phys. Lett. B202, 94
[3] Sevrin A., Troost J. (1997) Off-shell formulation of N = 2 non-linear sigma-models. Nucl. Phys. B492, 623 · Zbl 1004.81564
[4] Bogaerts J., Sevrin A., van der Loo S., Van Gils S. (1999) Properties of semichiral superfields. Nucl. Phys. B562, 277 · Zbl 0958.81194
[5] Curtright T.L., Zachos C.K. (1984). Geometry, topology and supersymmetry in nonlinear models. Phys. Rev. Lett. 53: 1799 · Zbl 1287.81045
[6] Howe P.S., Sierra G. (1984) Two-dimensional supersymmetric nonlinear sigma models with torsion. Phys. Lett. B148, 451
[7] Lyakhovich S., Zabzine M. (2002) Poisson geometry of sigma models with extended supersymmetry. Phys. Lett. B548, 243 · Zbl 0999.81044
[8] Hitchin N. (2003) Generalized calabi-yau manifolds. Q. J. Math. 54(3): 281–308 · Zbl 1076.32019
[9] Gualtieri, M. Generalized complex geometry. Oxford University, DPhil thesis, 2004 · Zbl 1079.53106
[10] Lindström U. (2004) Generalized N = (2,2) supersymmetric non-linear sigma models. Phys. Lett. B587, 216 · Zbl 1246.81375
[11] Lindström U., Minasian R., Tomasiello A., Zabzine M. (2005) Generalized complex manifolds and supersymmetry. Commun. Math. Phys. 257, 235 · Zbl 1118.53048
[12] Lindström U., Roček M., von Unge R., Zabzine M. (2005) Generalized Kaehler geometry and manifest N = (2,2) supersymmetric nonlinear sigma-models. JHEP 0507, 067
[13] Ivanov I.T., Kim B.B., Roček M. (1995) Complex structures, duality and WZW models in extended superspace. Phys. Lett. B343, 133
[14] Sevrin, A., Troost, J. The geometry of supersymmetric sigma-models. In: Proceedings of the workshop ”Gauge Theories, Applied Supersymmetry and Quantum Gravity”, London: Imperial college, 1996 · Zbl 1004.81564
[15] Grisaru M.T., Massar M., Sevrin A., Troost J. (1997) The quantum geometry of N = (2,2) non-linear sigma-models. Phys. Lett. B412, 53
[16] Hitchin N. (2006) Instantons, Poisson structures and generalized Kähler geometry. Commun. Math. Phys. 265, 131–164 · Zbl 1110.53056
[17] Arnold, V.I. Mathematical methods of classical mechanics. Translated from the Russian by K. Vogtmann and A. Weinstein. Second Edition. Graduate Texts in Mathematics, 60 New York Springer-Verlag, 1989
[18] Lindström, U., Roček, M. Private communication, in preparation
[19] Hitchin N.J., Karlhede A., Lindström U., Roček M. (1987) Hyperkähler Metrics And Supersymmetry. Commun. Math. Phys. 108, 535 · Zbl 0612.53043
[20] Vaisman I. (1994) Lectures on the Geometry of Poisson Manifolds, Progress in Mathematics, Vol. 118. Basel: Birkhäuser · Zbl 0810.53019
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