Proceeding from a nonlinear realization of the most general N =4, d=1 superconformal symmetry, associated with the supergroup D(2, 1; α), we construct a new model of nonrelativistic N =4 superconformal mechanics. In the bosonic sector it combines the worldline dilaton with the fields parametrizing the R-symmetry coset S 2 ∼ SU (2)/U (1). We present invariant off-shell N =4 and N =2 superfield actions for this system and show the existence of an independent N =4 superconformal invariant which extends the dilaton potential. The extended supersymmetry requires this potential to be accompanied by a d=1 WZW term on S 2 . We study the classical dynamics of the bosonic action and the geometry of its sigma-model part. It turns out that the relevant target space is a cone over S 2 for any non-zero α = ± 1 2 . The constructed model is expected to be related to the 'relativistic' N =4 mechanics of the AdS 2 × S 2 superparticle via a nonlinear transformation of the fields and the time variable.
Proceeding from nonlinear realizations of the most general N = 4, d = 1 superconformal symmetry associated with the supergroup D(2, 1; α), we construct all known and two new off-shell N = 4, d = 1 supermultiplets as properly constrained N = 4 superfields. We find plenty of nonlinear interrelations between the multiplets constructed and present a few examples of invariant superfield actions for them. The superconformal transformation properties of these multiplets are explicit within our method.
We construct a variety of off-shell N =8, d=1 supermultiplets with finite numbers of component fields as direct sums of properly constrained N =4, d=1 superfields. We also show how these multiplets can be described in N =8, d=1 superspace where the whole amount of supersymmetry is manifest. Some of these multiplets can be obtained by dimensional reduction from N =2 multiplets in d=4, whereas others cannot. We give examples of invariant superfield actions for the multiplets constructed, including N =8 superconformally invariant ones.
We construct new models of N=8 superconformal mechanics associated with the
off-shell N=8, d=1 supermultiplets (3,8,5) and (5,8,3). These two multiplets
are derived as N=8 Goldstone superfields and correspond to nonlinear
realizations of the N=8, d=1 superconformal group OSp(4^*|4) in its supercosets
OSp(4^*|4)/U(1)_R x SO(5) and OSp(4^*|4)/SU(2)_R x SO(4), respectively. The
irreducibility constraints for these superfields automatically follow from
appropriate superconformal covariant conditions on the Cartan superforms. The
N=8 superconformal transformations of the superspace coordinates and the
Goldstone superfields are explicitly given. Interestingly, each N=8
supermultiplet admits two different off-shell N=4 decompositions, with
different N=4 superconformal subgroups SU(1,1|2) and OSp(4^*|2) of OSp(4^*|4)
being manifest as superconformal symmetries of the corresponding N=4, d=1
superspaces. We present the actions for all such N=4 splittings of the N=8
multiplets considered.Comment: 31 pages, LaTeX, typos corrected, reference adde
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