Central extensions of supersymmetry in four and three dimensions

We consider the maximal central extension of the supertranslation algebra in d=4 and 3, which includes tensor central charges associated to topological defects such as domain walls (membranes) and strings. We show that for all N-extended super-algebras these charges are related to nontrivial configurations on the scalar moduli space. For N=2 theories obtained from compactification on Calabi–Yau threefolds, we give an explicit realization of the moduli-dependent charges in terms of wrapped branes.