Charge lattices and consistency of 6D supergravity

We extend the known consistency conditions on the low-energy theory of six-dimensional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 1 $\end{document} supergravity. We review some facts about the theory of two-form gauge fields and conclude that the charge lattice Γ for such a theory has to be self-dual. The Green-Schwarz anomaly cancellation conditions in the supergravity theory determine a sublattice of Γ. The condition that this sublattice can be extended to a self-dual lattice Γ leads to a strong constraint on theories that otherwise appear to be self-consistent.