Confining Strings in Supersymmetric Theories with Higgs Branches

TL;DR

This paper numerically investigates flux tubes in supersymmetric gauge theories with Higgs branches, confirming the accuracy of a logarithmic tension approximation and exploring the effects of long-range tails in generic vacua.

Contribution

It provides a numerical validation of the Evlampiev-Yung tension formula for strings in N=1 supersymmetric QED with Higgs branches, including long-range tail effects.

Findings

Numerical results agree with the Evlampiev-Yung tension formula.

Long-range tails are characteristic of generic Higgs branch vacua.

Finite string length L regularizes the long-range tails.

Abstract

We study flux tubes (strings) on the Higgs branches in supersymmetric gauge theories. In generic vacua on the Higgs branches strings were shown to develop long-range "tails" associated with massless fields, a characteristic feature of the Higgs branch (the only exception is the vacuum at the base of the Higgs branch). A natural infrared regularization for the above tails is provided by a finite string length L. We perform a numerical study of these strings in generic vacua. We focus on the simplest example of strings in N=1 supersymmetric QED with the Fayet-Iliopoulos term. In particular, we examine the accuracy of a logarithmic approximation (proposed earlier by Evlampiev and Yung) for the tension of such string solutions. In the Evlampiev-Yung formula the dependence of tension on the string length is logarithmic and the dependence on the geodesic length from the base of the Higgs branch is quadratic. We observe a remarkable agreement of our numerical results for the string tension with the Evlampiev-Yung analytic expression.