Dynamics of Strings between Walls

TL;DR

This paper investigates the dynamics of vortex-strings between domain walls in supersymmetric gauge theories, revealing non-normalizable modes, deriving effective Lagrangians, and demonstrating 90-degree scattering during collisions.

Contribution

It introduces two methods to analyze vortex-string dynamics, providing explicit effective Lagrangians and confirming their agreement for separated strings.

Findings

Center of mass modes are non-normalizable

Explicit effective Lagrangian derived using hypergeometric functions

Head-on collisions result in 90-degree scattering

Abstract

Configurations of vortex-strings stretched between or ending on domain walls were previously found to be 1/4 Bogomol'nyi-Prasad-Sommerfield(BPS) states in N=2 supersymmetric gauge theories in 3+1 dimensions. 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 explicitly obtain the effective Lagrangian, in terms of hypergeometric functions, 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.