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

Abstract

As was shown recently, non-Abelian vortex strings supported in four-dimensional $\mathcal{N}=2$ 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 $\mathcal{N}=2$ 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.

27 pages, 2 figures. arXiv admin note: text overlap with arXiv:1611.03111, arXiv:1605.08433

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• Critical Non-Abelian Vortex and Holography for Little String Theory
• NS Three-form Flux Deformation for the Critical Non-Abelian Vortex String
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• Some comments about emission channels of non abelian vortices
• 2d Sigma Models on Non-compact Calabi-Yau and $\mathcal{N}=2$ Liouville Theory
• Long Way to Ricci Flatness
• Supersymmetrising the GSY Soliton
• Critical Non-Abelian Vortex String and 2D N=2 Black Hole
• Dynamics of non-Abelian strings in supersymmetric gauge theories
• Quantizing a solitonic string
• Search for NS 3-form Flux Induced Vacua for the Critical Non-Abelian Vortex String