Studying Boojums in N=2 Theory with Walls and Vortices

TL;DR

This paper investigates BPS domain walls, flux tubes, and their junctions in N=2 Abelian gauge theory, calculating boojum energies and analyzing their interactions in various configurations.

Contribution

It provides the first detailed calculation of boojum energies in N=2 theories and compares effective (2+1)D and bulk (3+1)D perspectives.

Findings

Boojum energy diverges logarithmically in the infrared.

Consistent energy calculations in (2+1)D and (3+1)D frameworks.

Analysis of boojum interactions across different geometries.

Abstract

We study 1/2 BPS domain walls, 1/2 BPS flux tubes (strings) and their 1/4 BPS junctions. We consider the simplest example of N=2 Abelian gauge theory with two charged matter hypermultiplets which contains all of the above-listed extended objects. In particular, we focus on string-wall junctions (boojums) and calculate their energy. It turns out to be logarithmically divergent in the infrared domain. We compute this energy first in the (2+1)-dimensional effective theory on the domain wall and then, as a check, obtain the same result from the point of view of (3+1)-dimensional bulk theory. Next, we study interactions of boojums considering all possible geometries of string-wall junctions and directions of the string magnetic fluxes.