SU(2|1) mechanics and harmonic superspace

Abstract

We define the worldline harmonic SU(2|1) superspace and its analytic subspace as a deformation of the flat N=4, d=1 harmonic superspace. The harmonic superfield description of the two mutually mirror off-shell (4,4,0) SU(2|1) supermultiplets is developed and the corresponding invariant actions are presented, as well as the relevant classical and quantum supercharges. Whereas the σ-model actions exist for both types of the (4,4,0) multiplet, the invariant Wess-Zumino term can be defined only for one of them, thus demonstrating non-equivalence of these multiplets in the SU(2|1) case as opposed to the flat N=4, d=1 supersymmetry. A superconformal subclass of general SU(2|1) actions invariant under the trigonometric-type realizations of the supergroup D(2,1;α) is singled out. The superconformal Wess-Zumino actions possess an infinite-dimensional supersymmetry forming the centerless N=4 super Virasoro algebra. We solve a few simple instructive examples of the SU(2|1) supersymmetric quantum mechanics of the (4,4,0) multiplets and reveal the SU(2|1) representation contents of the corresponding sets of the quantum states.

0 + 37 pages, typos corrected, a reference updated

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Cited by in corpus (10)

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• Long multiplets in supersymmetric mechanics
• Deformed supersymmetric quantum mechanics with spin variables
• Deformed $\mathcal{N}=8$ mechanics of $(8,8,0)$ multiplets
• SU(2$|$1) supersymmetric mechanics on curved spaces
• A three-dimensional superconformal quantum mechanics with $sl(2|1)$ dynamical symmetry
• Hidden Supersymmetries of Deformed Supersymmetric Mechanics
• SU$(2|1)$ supersymmetric spinning models of chiral superfields