Two-dimensional N=8 supersymmetric mechanics in superspace

Abstract

We construct a two-dimensional N=8 supersymmetric quantum mechanics which inherits the most interesting properties of N=2, $d=4$ supersymmetric Yang-Mills theory. After dimensional reduction to one dimension in terms of field-strength, we show that only complex scalar fields from the $N=2, d=4$ vector multiplet become physical bosons in $d=1$. The rest of the bosonic components are reduced to auxiliary fields, thus giving rise to the {\bf (2, 8, 6)} supermultiplet in $d=1$. We construct the most general superfields action for this supermultiplet and demonstrate that it possesses duality symmetry extended to the fermionic sector of theory. We also explicitly present the Dirac brackets for the canonical variables and construct the supercharges and Hamiltonian which form a N=8 super Poincarè algebra with central charges. Finally, we discuss the duality transformations which relate the {\bf (2, 8, 6)} supermultiplet with the {\bf (4, 8, 4)} one.