Monopoles, Vortices, Domain Walls and D-Branes: The Rules of Interaction

TL;DR

This paper reviews various BPS solitons in non-abelian gauge theories, introduces new results on domain wall dynamics, and explores their interactions, including binding energies and soliton passage effects.

Contribution

It provides a comprehensive review of solitons in non-abelian gauge theories and presents new insights into their interactions and domain wall dynamics.

Findings

Existence of a classical binding energy for string endings on walls.

An index theorem for domain walls in non-abelian gauge theories.

Analysis of soliton interactions such as monopole-wall and wall-wall passage.

Abstract

Non-abelian gauge theories in the Higgs phase admit a startling variety of BPS solitons. These include domain walls, vortex strings, confined monopoles threaded on vortex strings, vortex strings ending on domain walls, monopoles threaded on strings ending on domain walls, and more. After presenting a self-contained review of these objects, including several new results on the dynamics of domain walls, we go on to examine the possible interactions of solitons of various types. We point out the existence of a classical binding energy when the string ends on the domain wall which can be thought of as a BPS boojum with negative mass. We present an index theorem for domain walls in non-abelian gauge theories. We also answer questions such as: Which strings can end on which walls? What happens when monopoles pass through domain walls? What happens when domain walls pass through each other?