Dynamics of non-Abelian strings in supersymmetric gauge theories

Abstract

This thesis is devoted to studying strong coupling phenomena (and confinement in particular) in supersymmetric gauge theories. The central object of investigation is the non-Abelian string that is responsible for the "instead-of-confinement" phase for monopoles in 4D ${\mathcal N} = 2$ supersymmetric QCD with the U($N$) gauge group and $N_f$ flavors of quark hypermultiplets, $N \leqslant N_f \leqslant 2 N$. Here it is shown that the non-Abelian strings and confined monopoles survive when we transition to the ${\mathcal N} = 1$ supersymmetric QCD. To this end we consider a mass term $\mu$ for the adjoint matter, and in the limit of large $\mu$ the bulk theory flows to ${\mathcal N} = 1$. We consider this transition both from the bulk point of view and from the world sheet theory, which is the two-dimensional $\mathbb{CP}(N-1)$ model. Survival of monopoles in the ${\mathcal N} = 1$ supersymmetric QCD is important for the "instead-of-confinement" phase, and also for the Seiberg-Witten picture of confinement. Apart from that, we also consider non-Abelian vortex strings in 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. 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. Moreover, we explicitly demonstrate the "instead-of-confinement" phase, when the screened quarks and gauge bosons of weak coupling are replaced by the confined monopole-antimonopole pairs of strong coupling. English version. Full text (Russian and English) is available at the official web page https://go.spbu.ru/20a2711 .