DOMAIN WALLS, LOCALIZATION AND CONFINEMENT: What Binds Strings Inside Walls

We study a mechanism that induces confinement inside domain walls. Condensates on the two vacua separated by the wall, if they are equivalent, can tunnel from one side to the other. They can create a current and trap a confining string inside the domain wall. Strings in the two vacua are attracted toward the domain wall and form a bound state with it.

We consider a simple toy model that realizes this mechanism. We also provide an example from the Seiberg-Witten theory where everything can be studied in the strong coupling regime using the dual effective action. We finally compare our findings with the previously studied wall with two different quark flavors and explain why here the discussed mechanism of confinement does not act.