Effective lagrangians on domain walls and other solitons

Maintaining the preserved supersymmetry helps to find the effective Lagrangian on the BPS background in gauge theories with eight supercharges. As concrete examples, we take 1/2 BPS domain walls. The Lagrangian is given in terms of the superfields with manifest four preserved supercharges and is expanded in powers of the slow-movement parameter λ Theo(λ0) gives the superfield form of the BPS equations, whereas all the fluctuation fields follow at o(λ¹). The effective Lagrangian is given by the density of the Kähler potential which emerges automatically from the (λexpansion making four preserved supercharges manifest. More complete account of our method and applications is given in [1] (hep-Th/0602289) in which the case of non-Abelian vortices is also worked out.