N=4 supersymmetric mechanics in harmonic superspace
Jul, 200330 pages
Published in:
- JHEP 09 (2003) 073
e-Print:
- hep-th/0307111 [hep-th]
Report number:
- ITP-UH-05-03
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Abstract: (arXiv)
We define N=4, d=1 harmonic superspace HR^{1+2|4} with an SU(2)/U(1) harmonic part, SU(2) being one of two factors of the R-symmetry group SU(2)xSU(2) of N=4, d=1 Poincar\'e supersymmetry. We reformulate, in this new setting, the models of N=4 supersymmetric quantum mechanics associated with the off-shell multiplets (3, 4, 1) and (4, 4, 0). The latter admit a natural description as constrained superfields living in an analytic subspace of HR^{1+2|4}. We construct the relevant superfield actions consisting of a sigma-model as well as a superpotential parts and demonstrate that the superpotentials can be written off shell in a manifestly N=4 supersymmetric form only in the analytic superspace. The constraints implied by N=4 supersymmetry for the component bosonic target-space metrics, scalar potentials and background one-forms automatically follow from the harmonic superspace description. The analytic superspace is shown to be closed under the most general N=4, d=1 superconformal group D(2,1;\alpha). We give its action on the analytic superfields comprising the (3, 4, 1) and (4, 4, 0) multiplets, reveal a surprising relation between the latter and present the corresponding superconformally invariant actions. The harmonic superspace approach suggests a natural generalization of these multiplets, with a [2(n+1), 4n, 2(n-1)] off-shell content for n>2.Note:
- 31 pages, LaTeX
- mechanics: classical
- supersymmetry
- superspace: harmonic
- superpotential
- analytic properties
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