Effective Lagrangians on Domain Walls and Other Solitons

TL;DR

This paper develops a method to derive effective Lagrangians for BPS domain walls in supersymmetric gauge theories, using superfield formalism and slow-movement expansion, revealing the structure of fluctuations and preserved supersymmetry.

Contribution

It introduces a systematic approach to obtain effective Lagrangians on BPS backgrounds with manifest supersymmetry using superfield formalism and lambda expansion.

Findings

Effective Lagrangian expressed via Kähler potential density.

Method applies to 1/2 BPS domain walls in theories with eight supercharges.

Framework also applicable to non-Abelian vortices as detailed in related work.

Abstract

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 lambda. The O(lambda^0) gives the superfield form of the BPS equations, whereas all the fluctuation fields follow at O(lambda^1). The effective Lagrangian is given by the density of the K"ahler potential which emerges automatically from the lambda expansion making four preserved supercharges manifest. More complete account of our method and applications is given in hep-th/0602289 in which the case of non-Abelian vortices is also worked out.