Formula omitted] mechanics of general [formula omitted] multiplets

Abstract

We construct the manifestly N = 4 supersymmetric off-shell superfield “master” action for any number n of the N = 4 supermultiplets ( 4 , 4 , 0 ) described by harmonic analytic superfields q + a ( ζ , u ) , a = 1 , … , 2 n , subjected to the most general harmonic constraints. The action consists of the sigma-model and Wess–Zumino parts. We present the general expressions for the target space metric, torsion and background gauge fields. The generic target space geometry is shown to be weak HKT (hyper-Kähler with torsion), with the strong HKT and HK ones as particular cases. The background gauge fields obey the self-duality condition. Our formulation suggests that the weak HKT geometry is fully specified by the two primary potentials: an unconstrained scalar potential L ( q + , q − , u ) | θ = 0 which is the θ = 0 projection of the superfield sigma-model Lagrangian, and a charge 3 harmonic analytic potential L + 3 a ( q + , u ) | θ = 0 coming from the harmonic constraint on q + a . The reductions to the strong HKT and HK geometries amount to simple restrictions on the underlying potentials. We also show, using the N = 2 superfield approach, that the most general bosonic target geometry of the N = 4 , d = 1 sigma models, of which the weak HKT geometry is a particular case, naturally comes out after adding the mirror ( 4 , 4 , 0 ) multiplets with different transformation laws under N = 4 supersymmetry and SO ( 4 ) R symmetry. Thus the minimal dimension of the target spaces exhibiting such a “weakest” geometry is 8, which corresponds to a pair of the mutually mirror ( 4 , 4 , 0 ) multiplets.