Abstract
The most general unconstrained superfield action for self-interactingN=2 matter hypermultiplets in analyticN=2 superspace is argued to produce a most generalN=2 hyper-Kähler σ-model after eliminating an infinite set of auxiliary fields. This suggests a new possibility of classifying hyper-Kähler metrics according to theN=2 analytic superfield self-interactions and provides an effective tool to compute these metrics explicitly. As the simplest example the U(2)-invariant quartic self-coupling of a singleq-hypermultiplet is analyzed and is shown to yield the familiar Taub-NUT metric. To see the geometric pattern directly in terms ofN=2 superfields we introduce a new on-shell representation ofq-hypermultiplets inN=2 harmonic superspace similar to the τ-description ofN=2 gauge theories. For the U(2)-example this formulation is checked to coincide with that by Sierra and Townsend.
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References
Zumino, B.: Supersymmetry and Kähler manifolds. Phys. Lett.87B, 203–206 (1979)
Alvarez-Gaume, L., Freedman, D.Z.: Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model. Commun. Math. Phys.80, 443–451 (1981)
Bagger, J., Witten, E.: Matter couplings inN=2 supergravity. Nucl. Phys. B222, 1–10 (1983)
Grisaru, M., Rocek, M., Karlhede, A.: The super-Higgs effect in superspace. Phys. Lett.120B, 110–119 (1982)
Nilles, H.P.: Supersymmetry, supergravity, and particle physics. Phys. Rep.110, 1–162 (1985)
del Aguila, F., Dugan, M., Grinstein, P., Hall, L., Ross, G., West, P.: Low-energy models with two supersymmetries. Nucl. Phys. B250, 225–251 (1985)
Curtright, T.L., Freedman, D.Z.: Nonlinear σ-models with extended supersymmetry in four dimensions. Phys. Lett.90B, 71–74 (1980)
Alvarez-Gaumé, L., Freedman, D.Z.: Ricci-flat Kähler manifolds and supersymmetry. Phys. Lett.94B, 171–173 (1980);
Morozov, A., Perelomov, A.: HyperKählerian manifolds and exact β-functions of two-dimensionalN=4 supersymmetric σ models. Preprint ITEP-131, Moscow, 1–56 (1984)
Lindstrom, U., Rocek, M.: Scalar-tensor duality andN=1, 2 nonlinear σ-models. Nucl. Phys. B222, 285–308 (1983)
Galperin, A., Ivanov, E., Kalitzin, S., Ogievetsky, V., Sokatchev, E.: UnconstrainedN=2 matter, Yang-Mills and supergravity theories in harmonic superspace. Class Quantum Grav.1, 469–498 (1984)
Galperin, A., Ivanov, E., Ogievetsky, V., Sokatchev, E.: Harmonic supergraphs. Green functions and Feynman rules and examples JINR prep-s E2-85-127, 1–24, and E2-85-128, 1–20
Sierra, C., Townsend, P.: The gauge-invariantN=2 supersymmetric σ-model with general scalar potential. Nucl. Phys. B233, 289–306 (1984)
The hyperKähler supersymmetric σ-model in six dimensions. Phys. Lett.124B, 497–500 (1983)
Eguchi, T., Gilkey, P., Hanson, A.: Gravitation, gauge theories, and differential geometry. Phys. Rep.66, 213–393 (1980)
Rosly, A., Schwarz, A.: Geometric origin of new unconstrained superfields. In: Proceedings of III Int. Seminar “Quantum Gravity” (Moscow, October 1984)
Eguchi, T., Hanson, A.: Self-dual solutions to Euclidean gravity. Ann. Phys.120, 82–106 (1979)
Galperin, A., Ivanov, E., Ogievetsky, V., Townsend, P.K.: Eguchi-Hanson type metrics from harmonic superspace. Preprint JINR-E2-85-732, 1–15 (submitted to Class Quantum Grav.)
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Communicated by S. W. Hawking
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Galperin, A., Ivanov, E., Ogievetsky, V. et al. Hyper-Kähler metrics and harmonic superspace. Commun.Math. Phys. 103, 515–526 (1986). https://doi.org/10.1007/BF01211764
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DOI: https://doi.org/10.1007/BF01211764