Collisions of domain walls in a supersymmetric model

Abstract

A collision of two parallel domain walls in a supersymmetric model is analyzed by using both the effective-Lagrangian approximation and a numerical solution to the equations of motion for the scalar components of the superfields involved. Two cases—that where a configuration belonging to the type of two parallel walls is saturated in the sense of Bogomol’nyi, Prasad, and Sommerfeld (BPS) and that where such a configuration is not BPS-saturated—are considered individually. For the first case, it is shown that, at low initial velocities, a collision of the walls is virtually an elastic reflection somewhat delayed in time. It is also demonstrated that, in this case, it is possible to introduce a collective variable that has the meaning of an internal parameter of the configuration and which can be treated as a dynamical (time-dependent) variable and to describe the dynamics of the system in terms of an effective Lagrangian. For the second case, it is found that, for collisions, there is a critical value of v _cr≈0.9120 for the initial velocity v _i. For v _i<v _cr, the reflection of the walls occurs, the vacuum between the walls remaining unchanged. For v _i>v _cr, the collision process is accompanied by a change in the vacuum state between the walls.