Dynamics of non-Abelian strings in supersymmetric gauge theories

TL;DR

This thesis investigates non-Abelian strings in supersymmetric gauge theories, demonstrating their persistence across different supersymmetry levels and revealing stringy baryons and confinement phases through field-theoretic methods.

Contribution

It provides new insights into the survival of non-Abelian strings and monopoles in ${ m N}=1$ theories and identifies a stringy baryon as a massless state in critical superstring behavior.

Findings

Non-Abelian strings and monopoles survive in ${ m N}=1$ supersymmetric QCD.

Identification of a stringy baryon as a massless BPS state.

Demonstration of the 'instead-of-confinement' phase replacing screened particles with monopole-antimonopole pairs.

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 .