Modified mode-expansion on a BPS wall related to the nonlinear realization

TL;DR

This paper introduces a modified mode-expansion method for bulk fields in a BPS domain wall, clarifying its relation to nonlinear realization approaches and ensuring symmetry preservation.

Contribution

It presents a novel modified mode-expansion technique that relates to nonlinear realization methods for deriving effective theories on BPS walls.

Findings

Clarified the relation between mode-expansion and nonlinear realization approaches.

Proposed a modification respecting broken Lorentz and U(1)_R symmetries.

Enhanced understanding of effective theory derivation on BPS walls.

Abstract

We propose a modified mode-expansion of the bulk fields in a BPS domain wall background to obtain the effective theory on the wall. The broken SUSY is nonlinearly realized on each mode defined by our mode-expansion. Our work clarifies a relation between two different approaches to derive the effective theory on a BPS wall, {\it i.e.} the nonlinear realization approach and the mode-expansion approach. We also discuss a further modification that respects the Lorentz and $U(1)_R$ symmetries broken by the wall.