Flux Tubes on Higgs Branches in SUSY Gauge Theories

TL;DR

This paper investigates flux tubes on curved Higgs branches in supersymmetric gauge theories, analyzing their structure, tension, and potential for transition into semilocal strings, with detailed examples in N=1 QED and N=2 QCD.

Contribution

It provides a detailed analysis of flux tubes on curved Higgs branches in SUSY gauge theories, including their internal structure and tension, with explicit solutions in N=1 and N=2 models.

Findings

Flux tubes exist on curved Higgs branches but are 'thick' with complex internal structure.

String tension is composed of BPS core and tail contributions.

Potential transition of flux tubes into semilocal strings related to phase transitions.

Abstract

We study flux tubes on Higgs branches with curved geometry in supersymmetric gauge theories. As a first example we consider N=1 QED with one flavor of charges and with Higgs branch curved by adding a Fayet-Iliopoulos (FI) term. We show that in a generic vacuum on the Higgs branch flux tubes exist but become ``thick''. Their internal structure in the plane orthogonal to the string is determined by ``BPS core'' formed by heavy fields and long range ``tail '' associated with light fields living on the Higgs branch. The string tension is given by the tension of ``BPS core'' plus contribution coming from the ``tail''. Next we consider N=2 QCD with gauge group SU(2)and two flavors of fundamental matter (quarks) with the same mass. We perturb this theory by the mass term for the adjoint field which to the leading order in perturbation parameter do not break N=2 supersymmetry and reduces to FI term. The Higgs branch has Eguchi-Hanson geometry. We work out string solution in the generic vacuum on the Higgs branch and calculate its string tension. We also discuss if these strings can turn into semilocal strings, the possibility related to the confinement/deconfinement phase transition.