N=4 mechanics of general (4,4,0) multiplets

作者：Delduc F^*; Ivanov E

来源：Nuclear Physics B, 2012, 855(3): 815-853.

DOI：10.1016/j.nuclphysb.2011.10.016

• Supersymmetry
• Geometry
• Superfield

We construct the manifestly N = 4 supersymmetric off-shell superfield "master" action for any number a of the N = 4 supermultiplets (4, 4, 0) described by harmonic analytic superfields q(+a) (zeta, u), a = 1, ... , 2n, 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-Kahler 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)vertical bar(theta=0) which is the theta = 0 projection of the superfield sigma-model Lagrangian, and a charge 3 harmonic analytic potential L(+3a)(q(+), u)vertical bar(theta=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.

• 出版日期2012-2-21