Abstract
We continue our study of 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in N=2 supersymmetric Abelian gauge theories in four dimensions. In this work, we numerically confirm that a boojum appearing at an end point of a string on a thick domain wall behaves as a magnetic monopole with a fractional charge in three dimensions. We introduce a "magnetic" scalar potential whose gradient gives magnetic fields. Height of the magnetic potential has a geometrical meaning that is shape of the domain wall. We find a semi-local extension of boojum which has an additional size moduli at an end point of a semi-local string on the domain wall. Dyonic solutions are also studied and we numerically confirm that the dyonic domain wall becomes an electric capacitor storing opposite electric charges on its skins. At the same time, the boojum becomes fractional dyon whose charge density is proportional to ${\vec E} \cdot {\vec B}$. We also study dual configurations with an infinite number of boojums and anti-boojums on parallel lines and analyze the ability of domain walls to store magnetic charge as magnetic capacitors. In understanding these phenomena, the magnetic scalar potential plays an important role. We study the composite solitons from the viewpoints of the Nambu-Goto and Dirac-Born-Infeld actions, and find the semi-local BIon as the counterpart of the semi-local Boojum.
Highlights
Introduction and summaryTopological solitons, which often appear in physical settings where local or global symmetry is spontaneously broken, are important to various fields in modern physics such as string theory, field theory, cosmology, nuclear physics and condensed matter physics
Second we study a numerical solution to a configuration of periodically aligned vortex strings attached to the domain wall
We find a semi-local boojum which appears at the endpoint of the semi-local vortex string [29] on the domain wall in the model with multiple flavors NF ≥ 3 with partially degenerate masses for the hypermultiplets
Summary
Topological solitons, which often appear in physical settings where local or global symmetry is spontaneously broken, are important to various fields in modern physics such as string theory, field theory, cosmology, nuclear physics and condensed matter physics. In the weak coupling limit, the domain wall becomes thick and has a fat internal layer where the U (1) gauge symmetry is almost restored In this situation we numerically confirm that the boojums can be identified with magnetic point-like sources with a fractional charge from the 3 + 1 dimensional viewpoint by taking the thickness of the domain walls into account. This kind of study was already performed for example, in [10, 11, 12, 30] In these previous works, as the low energy effective action, the DBI action (or its linearization) which is obtained by dualizing the internal moduli of the domain wall to the Abelian gauge field was studied. This is precisely counterpart of the Q-lump string ending on the domain wall in the strong gauge coupling limit in the original field theory.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
