BPS Saturated Domain Walls along a Compact Dimension

TL;DR

This paper studies BPS saturated domain walls in generalized Wess-Zumino models with a compact dimension, revealing multiple well-separated walls, localized modes, and their spectral properties across different space-time dimensions.

Contribution

It demonstrates the existence of multiple BPS domain walls along a compact dimension and analyzes their localized modes and spectral characteristics in various dimensions.

Findings

Multiple equidistant BPS walls exist at large circumference.

Light modes are exponentially suppressed by inter-wall distance.

Localized fermions exhibit chirality in (2+1) dimensions.

Abstract

Generalized Wess-Zumino models which admit topologically non-trivial BPS saturated configurations along one compact, spatial dimension are investigated in various dimensions of space-time. We show that, in a representative model and for sufficiently large circumference, there are BPS configurations along the compact dimension containing an arbitrary number of equidistant, well-separated domain walls. We analyze the spectrum of the bosonic and fermionic light and massless modes that are localized on these walls. The masses of the light modes are exponentially suppressed by the ratio of the distance between the walls and their width. States that are initially localized on one wall oscillate in time between all the walls. In (2+1) dimensions the ``chirality'' of localized, massless fermions is determined. In the (1+1)-dimensional case we show how the mass of certain classically BPS saturated solitons is lifted above the BPS bound by instanton tunneling.