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

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).

One figure, 37 pages

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Cited by in corpus (21)

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• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• On exact correlation functions of chiral ring operators in $2d$ $\mathcal{N}=(2,2)$ SCFTs via localization
• Flux Compactification for the Critical Non-Abelian Vortex and Quark Masses
• Critical Non-Abelian Vortex and Holography for Little String Theory
• Non-Abelian Vortex in Four Dimensions as a Critical Superstring
• Superstring limit of Yang-Mills theories
• NS Three-form Flux Deformation for the Critical Non-Abelian Vortex String
• 2d Sigma Models on Non-compact Calabi-Yau and $\mathcal{N}=2$ Liouville Theory
• Some comments about emission channels of non abelian vortices
• Superstring theories as low-energy limit of supergroup gauge theories
• Supersymmetrising the GSY Soliton
• Critical Non-Abelian Vortex String and 2D N=2 Black Hole
• Long Way to Ricci Flatness
• Heterotically Deformed Sigma Models on the World Sheet of Semilocal Strings in SQED
• Quantizing a solitonic string
• Search for NS 3-form Flux Induced Vacua for the Critical Non-Abelian Vortex String
• Dynamics of non-Abelian strings in supersymmetric gauge theories