Critical String from Non-Abelian Vortex in Four Dimensions

TL;DR

This paper demonstrates that certain non-Abelian vortex strings in a specific four-dimensional N=2 super-Yang-Mills theory can behave as critical fundamental strings, satisfying the Polchinski-Strominger criterion for ultraviolet completeness.

Contribution

It identifies a particular 4D bulk theory with a superconformal world-sheet theory that fulfills the conditions for a critical string, linking vortex dynamics to string theory.

Findings

The world-sheet theory is superconformal with a six-dimensional target space.

The vortex supports a critical Virasoro central charge.

The model satisfies the Polchinski-Strominger criterion for criticality.

Abstract

In a class of non-Abelian solitonic vortex strings supported in certain N=2 super-Yang-Mills theories we search for the vortex which can behave as a critical fundamental string. We use the Polchinski-Strominger criterion of the ultraviolet completeness. We identify an appropriate four-dimensional bulk theory: it has the U(2) gauge group, the Fayet-Iliopoulos term and four flavor hypermultiplets. It supports semilocal vortices with the world-sheet theory for orientational (size) moduli described by the weighted CP(2,2) model. The latter is superconformal. Its target space is six-dimensional. The overall Virasoro central charge is critical. We show that the world-sheet theory on the vortex supported in this bulk model is the bona fide critical string.