Manifestly supersymmetric effective Lagrangians on BPS solitons

Abstract

A systematic method to obtain the effective Lagrangian on the Bogomol'nyi-Prasad-Sommerfield background in supersymmetric gauge theories is worked out, taking domain walls and vortices as concrete examples. The Lagrangian in terms of the superfields with four preserved supercharges is expanded in powers of the slow-movement parameter $\ensuremath{\lambda}$. The expansion gives the superfield form of the Bogomol'nyi-Prasad-Sommerfield equations at $\mathcal{O}({\ensuremath{\lambda}}^{0})$, and all the fluctuation fields at $\mathcal{O}({\ensuremath{\lambda}}^{1})$. The density of the K\"ahler potential for the effective Lagrangian follows as an automatic consequence of the $\ensuremath{\lambda}$ expansion making (four preserved) supercharges manifest.