Non-Abelian vortex in four dimensions as a critical Superstring
M. Shifman a, A. Yunga,b,c
aWilliam I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455, USA
bNational Research Center "Kurchatov Institute", Petersburg Nuclear Physics Institute, Gatchina, 188300 St. Petersburg, Russia
cSt. Petersburg State University, 199034 St. Petersburg, Russia
We discuss recent progress in describing a
certain non-Abelian vortex string as a critical superstring on a conifold
some subtle points. This particular solitonic vortex is supported in
four-dimensional supersymmetric QCD with the U(2) gauge group,
Nf=4 quark flavors and the Fayet-Iliopoulos term.
Under certain conditions the non-Abelian vortex can become infinitely thin
can be interpreted as a critical ten-dimensional superstring. In addition to
translational moduli the non-Abelian vortex under consideration carries six
orientational and size moduli.
The vortex moduli dynamics are described by a two-dimensional sigma model
with the target space
where Y6 is a non-compact Calabi-Yau conifold.
The closed string states which emerge in four dimensions (4D) are identified
with hadrons of
4D bulk QCD. It turns out that most of the states arising from the
ten-dimensional graviton spectrum
are non-dynamical in 4D. A single dynamical massless hypermultiplet
associated with the deformation
of the complex structure of the conifold is found. It is interpreted as a
of the 4D theory (at strong coupling).