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 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 $E_d(Z)$.

v1: 35 pages; v2: minor corrections in section 4.1.2, many references added; v3: further discussion added on the conformal factor of the generalised metric in section 2 and on the Wick-rotation used to construct examples in section 6

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Cited by in corpus (8)

• The Geometry, Branes and Applications of Exceptional Field Theory
• $T$-folds from Yang-Baxter deformations
• Non-Abelian U-duality for membrane
• Weaving the Exotic Web
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Locally non-geometric fluxes and missing momenta in M-theory
• Currents, charges and algebras in exceptional generalised geometry