Confinement near Argyres–Douglas point in [formula omitted] QCD and low energy version of AdS/CFT correspondence

Abstract

We study Abrikosov–Nielsen–Olesen (ANO) flux tubes on the Higgs branch of N=2 QCD with SU(2) gauge group and N f =2 flavors of fundamental matter. In particular, we consider this theory near Argyres–Douglas (AD) point where the mass of monopoles connected by these ANO strings become small. In this regime the effective QED which describes the theory on the Higgs branch becomes strongly coupled. We argue that the appropriate description of the theory is in terms of long and thin flux tubes (strings) with small tension. We interpret this as another example of duality between field theory in strong coupling and string theory in weak coupling. Then we consider the non-critical string theory for these flux tubes which includes fifth (Liouville) dimension. We identify CFT at the AD point as UV fix point corresponding to AdS metric on the 5d “gravity” side. The perturbation associated with the monopole mass term creates a kink separating UV and IR behavior. We estimate the renormalized string tension and show that it is determined by the small monopole mass. In particular, it goes to zero at the AD point.