U-duality in three and four dimensions

Abstract

Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of 11-dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the [Formula: see text] and [Formula: see text] U-duality groups reduce to the [Formula: see text] and [Formula: see text] T-duality symmetry groups of the type IIA theory. As examples we dualise M2-branes, both black and extreme. We find that uncharged black M2-branes become charged under U-duality, generalising the Harrison transformation, while extreme M2-branes will become new extreme M2-branes. The resulting tension and charges are quantised appropriately if we use the discrete U-duality group [Formula: see text].