Timelike U-dualities in Generalised Geometry

Abstract

We study timelike U-dualities acting in three and four directions of 11-dimensional supergravity, which form the groups $SL(2)\times SL(3)$ and SL(5). Using generalised geometry, we find that timelike U-dualities, despite previous conjectures, do not change the signature of the spacetime. Furthermore, we prove that the spacetime signature must be $(-,+,...,+)$ when the U-duality modular group is either $\frac{SL(2)\times SL(3)}{SO(1,1)\times SO(2,1)}$ or $\frac{SL(5)}{SO(3,2)}$. We find that for some dual solutions it is necessary to include a trivector field which is related to the existence of non-geometric fluxes in lower dimensions. In the second part of the paper, we explicitly study the action of the dualities on supergravity solutions corresponding to M2-branes. For a finite range of the transformation, the action of $SL(2)\otimes SL(3)$ on the worldvolume of uncharged M2-branes charges them while it changes the charge of extreme M2-branes. It thus acts as a Harrison transformation. At the limits of the range, we obtain the "subtracted geometries" which correspond to an infinite Harrison boost. Outside this range the trivector field becomes non-zero and we obtain a dual solution that cannot be uniquely written in terms of a metric, 3-form and trivector. Instead it corresponds to a family of solutions linked by a local SO(1,1) rotation. The SL(5) duality is used to act on a smeared extreme M2-brane giving a brane-like solution carrying momentum in the transverse direction that the brane was delocalised along.

44 pages, citations added. V2, minor corrections in introduction. V3, published version (minor changes)

References in corpus (14)

• Double Field Theory
• Generalised Geometry for M-Theory
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• The gauge structure of generalised diffeomorphisms
• Duality orbits of non-geometric fluxes
• Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
• Large Gauge Transformations in Double Field Theory
• Flux Compactifications of M-Theory on Twisted Tori
• U-dual fluxes and Generalized Geometry
• Dual fields and E_{11}
• E11, generalised space-time and IIA string theory
• Subtracted Geometry From Harrison Transformations
• E11, generalised space-time and equations of motion in four dimensions

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• $T$-folds from Yang-Baxter deformations
• Remarks on the non-Riemannian sector in Double Field Theory
• Non-Riemannian geometry of M-theory
• A master exceptional field theory
• The rotation curve of a point particle in stringy gravity
• String Theory and non-Riemannian Geometry
• Non-relativistic duality and $T\bar{T}$ deformations
• Tri-vector deformations in $d=11$ supergravity
• Weaving the Exotic Web
• Non-abelian tri-vector deformations in d=11 supergravity
• Conserved Currents of Double Field Theory
• Non-abelian U-duality at work
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Black hole thermodynamics, stringy dualities and double field theory
• Locally non-geometric fluxes and missing momenta in M-theory
• Doubled strings, negative strings and null waves
• Identifying Riemannian singularities with regular non-Riemannian geometry
• A Kaluza-Klein Approach to Double and Exceptional Field Theory
• Higher Spin Double Field Theory : A Proposal