No abstract

Using the N =4 superspace approach in one dimension (time), we construct general N =8 supersymmetric mechanics actions for the multiplets (b, 8, 8−b) classified in hep-th/0406015, with the main focus on the previously unexplored cases of (8, 8, 0), (7, 8, 1) and (6, 8, 2) , as well as on (5, 8, 3) for completeness. N =8 supersymmetry of the action amounts to a harmonicity condition for the Lagrangian with respect to its superfield arguments. We derive the generic off-shell component action for the "root" multiplet (8,8, 0), prove that the actions for all other multiplets follow from it through automorphic dualities and argue that this hierarchical structure is universal. The bosonic target geometry in all cases is conformally flat, with a unique scalar potential (except for the root multiplet). We show that the N =4 superfield constraints respect the full R-symmetry and find the explicit realization of its quotient over the manifest R-symmetry on superfields and component fields. Several R-symmetric N =4 superfield Lagrangians with N =8 supersymmetry are either newly found or reproduced by a simple universal method.

We elaborate on four different types of twisted N = (4, 4) supermultiplets in the SU (2) × SU (2), 2D harmonic superspace. In the conventional N = (4, 4), 2D superspace they are described by the superfieldsq i a ,q i a ,q i a ,q i a subjected to proper differential constraints, (i, i, a, a) being the doublet indices of four groups SU (2) which form the full R-symmetry group SO(4) L × SO(4) R of N = (4, 4) supersymmetry. We construct the torsionful off-shell sigma model actions for each type of these multiplets, as well as the corresponding invariant mass terms, in an analytic subspace of the SU (2) × SU (2) harmonic superspace. As an instructive example, N = (4, 4) superconformal extension of the SU (2) × U (1) WZNW sigma model action and its massive deformation are presented for the multipletq i a . We prove that N = (4, 4) supersymmetry requires the general sigma model action of pair of different multiplets to split into a sum of sigma model actions of each multiplet. This phenomenon also persists if a larger number of non-equivalent multiplets are simultaneously included. We show that different multiplets may interact with each other only through mixed mass terms which can be set up for multiplets belonging to "self-dual" pairs (q i a ,q i a ) and (q i a ,q i a ) . The multiplets from different pairs cannot interact at all. For a "self-dual" pair of the twisted multiplets we give the most general form of the on-shell scalar potential.

We constructed the most general N = 4 superconformal 3-particles systems with translation invariance. In the basis with decoupled center of mass the supercharges and Hamiltonian possess one arbitrary function which defines all potential terms. We have shown that with the proper choice of this function one may describe the standard, A2 Calogero model as well as BC2, B2, C2 and D2 Calogero models with N = 4 superconformal symmetry. The main property of all these systems is that even with the coupling constant equal to zero they still contain nontrivial interactions in the fermionic sector. In other words, there are infinitely many non equivalent N = 4 supersymmetric extensions of the free action depending on one arbitrary function. We also considered quantization and explicitly showed how the supercharges and Hamiltonian are modified.

No abstract