Manifestly Supersymmetric Effective Lagrangians on BPS Solitons

TL;DR

This paper develops a systematic method to derive effective Lagrangians on BPS solitons in supersymmetric gauge theories, preserving supersymmetry explicitly and applying it to domain walls and vortices.

Contribution

It introduces a superfield expansion approach that maintains manifest supersymmetry and derives the effective Lagrangian and BPS equations systematically.

Findings

Superfield expansion yields BPS equations at leading order.

Effective Lagrangian density follows from lambda expansion.

Method applies to domain walls and vortices.

Abstract

A systematic method to obtain the effective Lagrangian on the BPS background in supersymmetric gauge theories is worked out, taking domain walls and vortices as concrete examples. The Lagrangian in terms of the superfields for four preserved SUSY is expanded in powers of the slow-movement parameter lambda. The expansion gives the superfield form of the BPS equations at {O}(lambda^0), and all the fluctuation fields at {O}(lambda^1). The density of the Kaehler potential for the effective Lagrangian follows as an automatic consequence of the lambda expansion with manifest (four preserved) SUSY.