U-duality in three and four dimensions

TL;DR

This paper explores how U-duality symmetries in 3 and 4 dimensions act on supergravity fields, comparing them with T-duality, and examines their effects on M2-branes, revealing new charged and extreme solutions.

Contribution

It demonstrates the reduction of U-duality groups to T-duality groups and analyzes the transformation of M2-branes under U-duality, including charge quantization.

Findings

U-duality groups reduce to T-duality groups in lower dimensions

Uncharged M2-branes become charged under U-duality

Extreme M2-branes transform into new extreme solutions

Abstract

Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of eleven dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the $SL(2)\otimes SL(3)$ and SL(5) U-duality groups reduce to the SO(2,2) and SO(3,3) 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 $E_d(Z)$.