Dimensional reduction of the ABJM model

We dimensionally reduce the ABJM model, obtaining a two-dimensional theory that can be thought of as a ‘master action’. This encodes information about both T- and S-duality, i.e. describes fundamental (F1) and D-strings (D1) in 9 and 10 dimensions. The Higgsed theory at large VEV, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \tilde{v} $\end{document}, and large k yields D1-brane actions in 9d and 10d, depending on which auxiliary fields are integrated out. For N = 1thereisamaptoa Green-Schwarz string wrapping a nontrivial circle in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{{\mathbb{C}^4}}} \left/ {{{\mathbb{Z}_k}}} \right.} $\end{document}.