D-brane charges in gravitational duals of 2 + 1 dimensional gauge theories and duality cascades

We perform a systematic analysis of the D-brane charges associated with string theory realizations of d = 3 gauge theories, focusing on the examples of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 4 $\end{document} supersymmetric U(N) × U(N + M) Yang-Mills theory and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 3 $\end{document} supersymmetric U(N) × U(N + M) Yang-Mills-Chern-Simons theory. We use both the brane construction of these theories and their dual string theory backgrounds in the supergravity approximation. In the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 4 $\end{document} case we generalize the previously known gravitational duals to arbitrary values of the gauge couplings, and present a precise mapping between the gravity and field theory parameters. In the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 3 $\end{document} case, which (for some values of N and M) flows to an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 6 $\end{document} supersymmetric Chern-Simons-matter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B2 field in the IR solution by 1/2, in units where its periodicity is one, compared to previous claims. We also suggest that the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 3 $\end{document} theories may exhibit, for some values of N and M, duality cascades similar to those of the Klebanov-Strassler theory.