Monin, Sergii2017-10-092017-10-092017-06http://hdl.handle.net/11299/190522University of Minnesota Ph.D. dissertation.June 2017. Major: Physics. Advisor: Mikhail Shifman. 1 computer file (PDF); viii, 86 pages.We study world-sheet theories of Abelian and non-Abelian strings that arise in different models. Considering a model in which Abelian (Abrikosov-Nielsen-Olesen) string acquires rotational (quasi)moduli we analyze the parameter space to find examples in which these strings not only coexist but are degenerate in tension. We prove that both solutions are locally stable, i.e there are no negative modes in the string background. The tension degeneracy is achieved at the classical level and is expected to be lifted by quantum corrections. Moreover, using a representative set of parameters we numerically calculate the low-energy Lagrangian on the world sheet of the Abrikosov-Nielsen-Olesen string. The bulk model is deformed by a spin-orbit interaction generating a number of ``entangled" terms on the string world sheet. We also consider modifications of ${\mathcal N}=2\;$ supersymmetric QCD with the U$(N)$ gauge group and $N_f=N$ quark flavors. These models support non-Abelian strings. The dynamics of the orientational modes is described by two-dimensional CP$(N-1)$ model with varying degrees of supersymmetry. We used analytical methods to solve the CP$(N-1)\;$ model at finite string length $L$ assuming periodic boundary conditions. In the pure bosonic theory in the large-$N$ limit we detect a phase transition at $L\sim \Lambda_{\rm CP}^{-1}$ (which is expected to become a rapid crossover at finite $N$). At large $L$ the CP$(N-1)$ model develops a mass gap and is in the Coulomb/confinement phase, while at small $L$ it is in the deconfinement phase. In the ${\mathcal N}=(2,2)\;$ supersymmetric CP$(N-1)$ model at finite $L$ we find a large-$N$ solution which was not known previously. We use the power of holomorphy to deduce that the theory has a single phase independently of the value of $L\Lambda_{\rm CP}$. For any value of this parameter a mass gap develops and supersymmetry remains unbroken. So does the $SU(N)$ symmetry of the target space. In the heterotic ${\mathcal N}=(0,2)\;$ CP$(N-1)\;$ model we find a rich phase structure and discuss how it matches the ${\mathcal N}=(2,2)\;$ limit.enConfinementLarge-NStringsThesis or Dissertation