Non-Abelian Vortex in Four Dimensions as a Critical String on a Conifold

TL;DR

This paper explores how non-Abelian vortex strings in a four-dimensional N=2 Yang-Mills theory can be viewed as critical superstrings on a conifold, revealing a connection between string states and 4D hadrons, including a monopole-monopole baryon.

Contribution

It demonstrates that non-Abelian vortex strings in a specific 4D gauge theory can be described as critical superstrings on a conifold, identifying associated 4D hadronic states.

Findings

Most string-derived states are non-dynamical in 4D.

Identifies a massless hypermultiplet from conifold deformation.

Interprets this hypermultiplet as a monopole-monopole baryon.

Abstract

Non-Abelian vortex strings supported in a certain four-dimensional N=2 Yang-Mills theory with fundamental matter were shown arXiv:1502.00683 to become critical superstrings. In addition to translational moduli non-Abelian string under consideration carries orientational and size moduli. Their dynamics is described by two-dimensional sigma model whose target space is a tautological bundle over the complex projective space. For the N=2 theory with the $U(2)$ gauge group and four fundamental hypermultiplets there are six orientational and size moduli. After combining with four translational moduli they form a ten-dimensional target space required for a superstring to be critical. For the theory in question the target space of the sigma model is C^2 x Y_6, where Y_6 is a conifold. We study closed string states which emerge in four dimensions (4D) and identify them with hadrons of the 4D bulk N=2 theory. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. We find a single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold. We interpret this degree of freedom as a monopole-monopole baryon of the 4D theory (at strong coupling).