# Critical Non-Abelian Vortex in Four Dimensions and Little String Theory

## TL;DR

This paper explores the critical non-Abelian vortex strings in four-dimensional supersymmetric QCD, identifying their spectrum of states and relating them to hadrons and monopole configurations, thus connecting string theory with gauge theory phenomena.

## Contribution

It demonstrates the emergence of a critical superstring from non-Abelian vortex strings in 4D ${
m N}=2$ SQCD and identifies massive states as monopole necklaces, extending the understanding of string-gauge dualities.

## Key findings

- Identification of massive closed string states in 4D
- Massless state as deformation of the conifold
- Interpretation of states as monopole necklaces

## Abstract

As was shown recently, non-Abelian vortex strings supported in four-dimensional ${\cal N}=2$ supersymmetric QCD with the U(2) gauge group and $N_f=4$ quark multiplets (flavors) become critical superstrings. In addition to the translational moduli non-Abelian strings under consideration carry six orientational and size moduli. Together they form a ten-dimensional target space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space and a Calabi-Yau non-compact threefold, namely, the conifold. We study closed string states which emerge in four dimensions (4D) and identify them with hadrons of four-dimensional ${\cal N}=2$ QCD. One massless state was found previously: it emerges as a massless hypermultiplet associated with the deformation of the complex structure of the conifold. In this paper we find a number of massive states. To this end we exploit the approach used in LST, "Little String Theory," namely equivalence between the critical string on the conifold and non-critical $c=1$ string with the Liouville field and a compact scalar at the self-dual radius. The states we find carry "baryonic" charge (its definition differs from standard). We interpret them as "monopole necklaces" formed (at strong coupling) by the closed string with confined monopoles attached.