Resumo
Using the worldline SU(2|1) superfield approach, we construct N = 4 superconformally
invariant actions for the d = 1 multiplets (1, 4, 3) and (2, 4, 2). The SU(2|1) superfield
framework automatically implies the trigonometric realization of the superconformal
symmetry and the harmonic oscillator term in the corresponding component actions. We
deal with the general N = 4 superconformal algebra D(2, 1; ) and its central-extended
= 0 and = −1 psu(1, 1|2) ⊕su(2) descendants. We capitalize on the observation that
D(2, 1; ) at 6= 0 can be treated as a closure of its two su(2|1) subalgebras, one of which
defines the superisometry of the SU(2|1) superspace, while the other is related to the first
one through the reflection of μ, the parameter of contraction to the flat N = 4, d = 1
superspace. This closure property and its = 0 analog suggest a simple criterion for
the SU(2|1) invariant actions to be superconformal: they should be even functions of μ.
We find that the superconformal actions of the multiplet (2, 4, 2) exist only at = −1, 0
and are reduced to a sum of the free sigma-model type action and the conformal superpotential
yielding, respectively, the oscillator potential ∼ μ2 and the standard conformal
inverse-square potential in the bosonic sector. The sigma-model action in this case can
be constructed only on account of non-zero central charge in the superalgebra su(1, 1|2).
PACS: 03.65.-