Flux tubes on Higgs branches in SUSY gauge theories

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 FayetIliopoulos (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 N f = 2 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.

Non-Abelian strings in N=1 supersymmetric QCD

“…Note, that the logarithmic suppression of the string tension is not specific for non-Abelian strings. Similar expression was found for the ANO string on a Higgs branch [26,27].…”

“…In many instances this breaking provides topological reasons behind formation of vortex strings. A dynamical side of the problem of the vortex string formation in theories with Higgs branches was addressed in [25,26,27]. A priori it is not clear at all whether or not stable string solutions exist in this class of theories.…”

“…In particular, it was shown in [25] that infinitely long strings cannot be formed in this case due to infrared divergences. Later this problem was studied in [26,27]. It was shown that vortices on Higgs branches become logarithmically "thick" due to the presence of massless scalars in the bulk.…”

“…Another way of IR regularization is to lift the Higgs branch so that scalar fields forming the string have small but non-zero masses m L , cf. [27]. We use this approach here, see Eqs.…”

Supersymmetric solitons

“…The BPS string solutions exist only on the base manifold of the Higgs branch. The flux tubes become non-BPS-saturated if we move in non-compact directions [162]. Therefore, we will limit ourselves to the vacua which belong to the base manifold.…”