Gauging isometries in N=4 supersymmetric mechanics

This talk summarizes the study of superfield gaugings of isometries of extended supersymmetric mechanics in hep-th/0605211, hep-th/0611247 and arXiv:0706.0706. The gauging procedure provides a manifestly supersymmetric realization of d=1 automorphic dualities which interrelate various irreducible off-shell multiplets of d=1 extended supersymmetry featuring the same number of physical fermions but different divisions of bosonic fields into the physical and auxiliary subsets. We concentrate on the most interesting N=4 case and demonstrate that, with a suitable choice of the symmetry to be gauged, all such multiplets of N=4 supersymmetric mechanics and their generic superfield actions can be obtained from the "root" multiplet (4,4,0) and the appropriate gauged subclasses of the generic superfield action of the latter by a simple universal recipe.