Bogomol'nyi-Prasad-Sommerfield saturated domain walls along a compact dimension - art. no. 025017

Generalized Wess-Zumino models which admit topologically non-trivial BPS sa turated configurations along one compact, spatial dimension are investigate d in various dimensions of space-time. We show that, in a representative mo del and for a sufficiently large circumference, there are BPS configuration s along the compact dimension containing an arbitrary number of equidistant , well-separated domain walls. We analyze the spec trum of the bosonic and fermionic light and massless modes that are localized on these walls. The m asses of the light modes are exponentially suppressed by the ratio of the d istance between the walls and their width. States that are initially locali zed 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.