Notes on Vortices and String/Gauge Theory Correspondence

In this notes we consider relations between strings, vortices, and 2D gauge theories. The framework we study these relations is string/gauge theory dualities. We show that certain quantities satisfy Toda equations. Next, we show that the brane construction of non-Abelian cortices can be embedded into ABJM theory and thus, it contains non-Abelian vortex solutions.