Flux Tubes on Higgs Branches in SUSY Gauge Theories

TL;DR

This work analyzes flux tubes on curved Higgs branches in SUSY gauge theories, showing that flux tubes persist even when massless Higgs modes exist, but acquire a logarithmic dependence on string length due to a light-tail along the Higgs branch. The authors study two principal setups: an ${\cal N}=1$ QED with a Fayet–Iliopoulos term producing a two-dimensional hyperbolic Higgs branch, and an ${\cal N}=2$ SU(2) QCD with two equal-mass flavors whose Higgs branch has Eguchi–Hanson geometry, perturbing by an adjoint mass that preserves leading ${\cal N}=2$ structure and yields a curved Higgs branch; in both cases flux tubes consist of a heavy-field BPS core and a tail from light moduli, with the string tension given by $T=T_{\text{core}}+T_{\text{tail}}$. For generic vacua the strings are non-BPS, and the tail introduces a logarithmic correction $T_{\text{tail}}\propto l^2/\log(1/(m_L R_c))$, leading to a confinement potential $V(L)\sim L/\log L$, whereas at the base cycle the strings become semilocal and can drive a confinement–deconfinement transition. The analysis connects the microphysics of flux tubes to the global geometry of Higgs branches (hyperbolic and Eguchi–Hanson) and highlights how SUSY structure and IR regularization control the existence, stability, and confinement properties of string configurations.

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.