Stringy effects in four-dimensional N = 2 supersymmetric QCD from 2D-4D correspondence

AIP Conference Proceedings. 2021. No. 2377. Article 090002.

Ievlev E. A., Yung A., Shifman M.

In this talk we are going to discuss recent results on 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. 
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It has been recently shown that these vortices behave as critical superstrings. 
In particular, the lowest  string state appears to be a massless BPS ``baryon." 

Here we confirm the existence of this stringy baryon using purely field-theoretic methods. 
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. 
Then we use the 2D-4D correspondence to show that a marginal deformation of the target space 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.
Moreover, we explicitly demonstrate the occurrence of the so-called \textquote{instead-of-confinement} phase.

Based on the talk given at the XXIV International Scientific Conference of Young Scientists and Specialists (AYSS-2020).

Keywords: суперсимметрия, supersymmetry, confinement, конфайнмент