Hadrons in $\mathcal{N}=2$ supersymmetric QCD from non-Abelian string on 2D black hole

TL;DR

This paper explores the spectrum of hadrons in 4D $ ext{N}=2$ supersymmetric QCD using non-Abelian strings modeled as critical superstrings on a 2D supersymmetric black hole, revealing a phase transition between Higgs and string phases.

Contribution

It extends the analysis of non-Abelian vortex strings to $U(N)$ gauge theories with even $N$ and $2N$ flavors, connecting hadron spectra to string theory on a 2D black hole and clarifying phase transitions.

Findings

Hadron spectrum matches string spectrum on 2D black hole.

Confirmed multiplicity of hadronic states from string and field theory.

Identified phase transition as a conifold transition in string theory.

Abstract

We continue the study of non-Abelian vortex string in 4D $\mathcal{N}=2$ supersymmetric QCD as critical superstring, and extend this analysis to $U(N)$ gauge theory with arbitrary even $N$ and $N_f=2N$ number of quarks. We introduce a special mass deformation and show that the SQCD hadron spectrum is still given by the string spectrum on the 2D $\mathcal{N}=2$ supersymmetric black hole. We perform a cross-check by computing the multiplicity of hadronic states of the high-energy part of the spectrum both from string and field theory pictures. We also clarify the spontaneous breaking of the global flavor symmetry by VEV of the massless baryon. We finally claim, that phase diagram of $\mathcal{N}=2$ SQCD with $N_f=2N$ consists of the Higgs phase at weak coupling and string/hadronic phase at strong coupling, separated by phase transition, and is seen as a conifold transition from string theory point of view.