2D Seiberg-like dualities with an adjoint matter

We consider the analogue of Kutasov-Schwimmer-Seiberg duality for two-dimensional N=22Uk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=\left(2,2\right)U(k) $$\end{document} gauge theory with one adjoint X with the superpotential Tr Xl+1 and with fundamental and anti-fundamental chiral multiplets. We give the evidences for the proposed dualities by analytically proving that the elliptic genus of dual pair coincides with each other. For some of the dual pairs flowing to the superconformal field theory, we show the nonperturbative truncation of the chiral ring. For the theory with one adjoint and Nf > k fundamental fields, we argue the theory exhibits mass gap.