Abstract
We study non-Abelian vortex strings in four-dimensional (4D) $\mathcal{N} = 2$ supersymmetric QCD with U$(N=2)$ gauge group and $N_f=4$ flavors of quark hypermultiplets. It has been recently shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D $\mathcal{N} = 2$ supersymmetric QCD. In particular, the lowest string state appears to be a massless BPS "baryon." Here we show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we study the conformal world-sheet theory on the non-Abelian string -- the so called weighted $\mathcal{N} = (2,2)$ supersymmetric $\mathbb{CP}$ model. Its target space is given by the six-dimensional non-compact Calabi-Yau space $Y_6$, the conifold. We use mirror description of the model to study the BPS kink spectrum and its transformations on curves (walls) of marginal stability. Then we use the 2D-4D correspondence to show that the deformation of the complex structure of the conifold is associated with the emergence of a non-perturbative Higgs branch in 4D theory which opens up at strong coupling. The modulus parameter on this Higgs branch is the vacuum expectation value of the massless BPS "baryon" previously found in string theory.
Highlights
In 2015 a non-Abelian semilocal vortex string was discovered possessing a world-sheet theory that is both superconformal and critical [1]
At each step we determine which kinks decay on CMS and which are stable upon crossing and establish their relation to four-dimensional monopoles using the so-called 2D-4D correspondence, the coincidence of BPS spectra in 4D N 1⁄4 2 SQCD, and in the string world-sheet theory [6,7,11]
This phase is qualitatively similar to the conventional QCD confinement: the quarks and gauge bosons screened at weak coupling, at strong coupling evolve into monopole-antimonopole pairs confined by non-Abelian strings
Summary
In 2015 a non-Abelian semilocal vortex string was discovered possessing a world-sheet theory that is both superconformal and critical [1]. At each step we determine which kinks decay on CMS and which are stable upon crossing and establish their relation to four-dimensional monopoles using the so-called 2D-4D correspondence, the coincidence of BPS spectra in 4D N 1⁄4 2 SQCD, and in the string world-sheet theory [6,7,11]. At strong coupling we use 2D-4D correspondence to confirm that our 4D SQCD enters the so-called “instead-ofconfinement” phase found earlier in asymptotically free versions of SQCD [12]; see [13] for a review This phase is qualitatively similar to the conventional QCD confinement: the quarks and gauge bosons screened at weak coupling, at strong coupling evolve into monopole-antimonopole pairs confined by non-Abelian strings.
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