Non-Abelian vortex strings supported in a certain four-dimensional N=2 Yang-Mills theory with fundamental matter were shown  to become critical superstrings. In addition to translational moduli, the non-Abelian strings under consideration carry orientational and size moduli. Their dynamics is described by the 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, which is required for a superstring to be critical. For the theory in question, the target space of the sigma model is C2×Y6, where Y6 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 nondynamical 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).
Bibliographical noteFunding Information:
This work is supported in part by DOE Grant No.DE-SC0011842. The work of A.Y. was supported by the William I. Fine Theoretical Physics Institute of the University of Minnesota, and by the Russian State Grant for Scientific Schools No.RSGSS-657512010.2. The work of A.Y. was supported by the Russian Scientific Foundation under Grant No.14-22-00281. P.K. would also like to thank the W. Fine Institute for Theoretical Physics at the University of Minnesota for kind hospitality during his visit, where part of this work was done. The research of P.K. was supported in part by the Perimeter Institute for Theoretical Physics. Research at the Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation.
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