Dynamics of Strings between Domain Walls

TL;DR

This paper investigates the dynamics of vortex-strings between domain walls using moduli space and effective action methods, revealing non-normalizable zero modes and 90-degree scattering during collisions.

Contribution

It provides the first explicit effective Lagrangian for vortex-string dynamics between domain walls and compares two approximation methods, confirming their agreement.

Findings

Non-normalizable zero modes of string center of mass.

Explicit effective Lagrangian for string dynamics.

90-degree scattering in head-on collisions.

Abstract

Configurations of vortex-strings stretched between or ending on domain walls were previously found to be 1/4 BPS states. Among zero modes of string positions, the center of mass of strings in each region between two adjacent domain walls is shown to be non-normalizable whereas the rests are normalizable. We study dynamics of vortex-strings stretched between separated domain walls by using two methods, the moduli space (geodesic) approximation of full 1/4 BPS states and the charged particle approximation for string endpoints in the wall effective action. In the first method we obtain the effective Lagrangian explicitly and find the 90 degree scattering for head-on collision. In the second method the domain wall effective action is assumed to be U(1)^N gauge theory, and we find a good agreement between two methods for well separated strings. This paper is based on our paper arXiv:0810.3495 [hep-th].