Abstract
We define the basics of (4, 4) 2 D harmonic superspace with two independent sets of SU(2) harmonic variables and apply it to constructing new superfield actions of (4, 4) supersymmetric two-dimensional sigma models with torsion and mutually commuting left and right complex structures, as well as of their massive deformations. We show that the generic off-shell sigma model action is the general action of constrained analytic superfields q (1,1) representing twisted N = 4 multiplets in (4, 4) harmonic superspace. The massive term of q (1,1) is shown to be unique; it generates a scalar potential the form of which is determined by the metric on the target bosonic manifold. We discuss in detail the (4, 4) supersymmetric group manifold SU(2) × U(1) WZNW sigma model and its Liouville deformation. A deep analogy of the relevant superconformally invariant analytic superfield action to that of the improved tensor N = 2 4 D multiplet is found. We define the (4, 4) duality transformation and find new off-shell dual representations of the previously constructed actions via unconstrained analytic (4, 4) superfields. The main peculiarities of the (4, 4) duality transformation are: (i) it preserves manifest (4, 4) supersymmetry; (ii) dual actions reveal a gauge invariance needed for the on-shell equivalence to the original description; (iii) in the actions dual to the massive ones, 2 D supersymmetry is modified off shell by SU(2) tensor central charges. The dual representation suggests some hints of how to describe (4, 4) models with non-commuting complex structures in the harmonic superspace.
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