Nonnormalizable Zero Modes on BPS Junctions

TL;DR

This paper investigates Nambu-Goldstone modes on BPS domain wall junctions in four-dimensional N=1 supersymmetric theories, revealing their non-normalizable nature and pairing structure, and proposing this as a general phenomenon.

Contribution

It demonstrates that Nambu-Goldstone modes on domain wall junctions are non-normalizable and extends the analysis to generic flat space in any dimensions.

Findings

Nambu-Goldstone modes extend infinitely along the wall

Modes come in pairs with the same mass, except for massless modes

Massless modes can appear singly, consistent with supersymmetry

Abstract

Using an exact solution as a concrete example, Nambu-Goldstone modes on the BPS domain wall junction are worked out for N=1 supersymmetric theories in four dimensions. Their wave functions extend along the wall to infinity (not localized) and are not normalizable. It is argued that this feature is a generic phenomenon of Nambu-Goldstone modes on domain wall junctions in the bulk flat space in any dimensions. We formulate mode equations and show that fermion and boson with the same mass come in pairs except massless modes which can appear singly, in accordance with unitary representations of (1, 0) supersymmetry.