Abstract
This contribution follows the talk, given by F. Delduc at the conference SQS’2011 in Dubna, Russia (July 18–23, 2011). To a considerable extent it is a summary of known facts about the links between geometry and extended supersymmetry in d = 1 mechanics, with emphasis on the harmonic superspace method created in Dubna in the 80’s. Some recent developments based on [1] are also presented.
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References
F. Delduc and E. A. Ivanov, “N = 4 Mechanics of General (4, 4, 0) Multiplets,” Nucl. Phys. B 855, 815 (2012). arXiv:1107.1429 [hep-th]
L. Alvarez-Gaumé and D. Z. Freedman, “Geometrical Structure and Ultraviolet Finiteness in the Supersymetric σ Model,” Commun. Math. Phys. 80, 443 (1981).
R. A. Coles and G. Papadopoulos, “The Geometry of the One-Dimensional Supersymmetric Nonlinear Sigma Models,” Classical Quantum Gravity 7, 427 (1990).
C. M. Hull, “The Geometry of Supersymmetric Quantum Mechanics,” QMW-99-16 (1999). arXiv:hepth/9910028
E. A. Ivanov and A. V. Smilga, “Dirac Operator on Complex Manifolds and Supersymmetric Quantum Mechanics” (2010). arXiv:1012.2069 [hep-th].
B. Zumino, “Supersymmetry and Kähler Manifolds,” Phys. Lett. B 87, 203 (1979).
C. M. Hull and E. Witten, “Supersymmetric Sigma Models and the Heterotic String,” Phys. Lett. B 160, 398 (1985).
A. Galperin, E. Ivanov, V. Ogievetsky, and E. Sokatchev, “Hyper-Kähler Metrics and Harmonic Superspace,” Commun. Math. Phys. 103, 515 (1986).
F. Delduc, S. Kalitzin, and E. Sokatchev, “Geometry of Sigma Models with Heterotic Supersymmetry,” Classical Quantum Gravity 7, 1567 (1990).
A. Galperin, E. Ivanov, V. Ogievetsky, and E. Sokatchev, “Harmonic Superspace as a Key to N=2 Supersymetric Theories // J. Exp. Theor. Phys. Lett. 40, 912 (1984); A. S. Galperin, E. A. Ivanov, S. Kalitzin, V. I. Ogievetsky, and E. S. Sokatchev, “Unconstrained N = 2 Matter, Yang-Mils and Supergravity Theories in Harmonic Superspace,” Classical Quantum Gravity 1, 469 (1984).
A. S. Galperin, E. A. Ivanov, V. I. Ogievetsky, and E. S. Sokatchev, Harmonic Superspace (Cambridge Univ. Press, Cambridge, 2001).
A. Galperin, E. Ivanov, V. Ogievetsky, and E. Sokatchev, “N = 2 Supergravity in Superspace: Different Versions and Matter Couplings,” Classical Quantum Gravity 4, 1255 (1987).
P. Howe and G. Papadopoulos, “Twistor Spaces for Hyper-Kähler Manifolds with Torsion,” Phys. Lett. B 379, 80 (1996).
C. G. Callan, J. A. Harvey, and A. Strominger, “World Sheet Approach to Heterotic Instantons and Solitons,” Nucl. Phys. B 359, 611 (1991).
J. Michelson and A. Strominger, “The Geometry of (Super)Conformal Quantum Mechanics,” Commun. Math. Phys. 213, 1 (2000). arXiv:hep-th/9907191
E. Ivanov and O. Lechtenfeld, “N=4 Supersymmetric Mechanics in Harmonic Superspace,” J. High Energy Phys. 0309, 073 (2003). arXiv:hep-th/0307111
E. Ivanov, O. Lechtenfeld, and A. Sutulin, “Hierarchy of N = 8 Mechanics Models,” Nucl. Phys. B 790, 493 (2008). arXiv:0705.3064 [hep-th]
G. W. Gibbons, G. Papadopoulos, and K. S. Stelle, “HKT and OKT Geometries on Soliton Black Hole Moduli Spaces,” Nucl. Phys. B 508, 623 (1997). arXiv:hep-th/9706207
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Delduc, F., Ivanov, E. Geometry and harmonic superspace: Some recent progress. Phys. Part. Nuclei 43, 562–568 (2012). https://doi.org/10.1134/S1063779612050097
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DOI: https://doi.org/10.1134/S1063779612050097