Timelike U-dualities in Generalised Geometry

Emanuel Malek

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Timelike U-dualities in Generalised Geometry

Emanuel Malek

High Energy Physics - Theory · Submitted 3 Jan 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using generalised geometry, we find that timelike U-dualities, despite previous conjectures, do not change the signature of the spacetime.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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).	contribution 0.92	0.82	0.06	asserted 0.99
s1	Using generalised geometry, we find that timelike U-dualities, despite previous conjectures, do not change the signature of the spacetime.	result 0.99	0.95	0.52	asserted 1.00
s2	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 $\frac{SL(5)}{SO(3,2)}$.	result 1.00	0.93	0.37	asserted 1.00
s3	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.	result 0.99	0.95	0.06	asserted 0.99
s4	In the second part of the paper, we explicitly study the action of the dualities on supergravity solutions corresponding to M2-branes.	contribution 0.99	0.94	0.04	asserted 1.00
s5	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.	result 1.00	0.93	0.07	asserted 1.00
s6	It thus acts as a Harrison transformation.	interpretation 0.92	0.79	0.05	asserted 1.00
s7	At the limits of the range, we obtain the "subtracted geometries" which correspond to an infinite Harrison boost.	result 0.97	0.89	0.05	asserted 1.00
s8	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.	result 1.00	0.92	0.05	asserted 1.00
s9	Instead it corresponds to a family of solutions linked by a local SO(1,1) rotation.	result 0.92	0.87	0.06	asserted 1.00
s10	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.	result 0.82	0.94	0.08	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original 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.

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References

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Classification of non-Riemannian doubled-yet-gauged spacetime
hep-th 2017-07 accept novelty 6.0 of 10

Every non-Riemannian Double Field Theory background is classified by two integers (n, n̄), with Newton-Cartan, Carroll, and Gomis-Ooguri geometries appearing as special cases.
Dynamics of Perturbations in Double Field Theory & Non-Relativistic String Theory
hep-th 2015-08 accept novelty 6.0 of 10

The Gomis-Ooguri non-relativistic closed string is shown to be a non-Riemannian Double Field Theory background whose sigma model and fluctuation spectrum match the Gomis-Ooguri results.
Geometry and fluxes of SL(5) exceptional field theory
hep-th 2014-12 accept novelty 6.0 of 10

The generalised torsion of a flat Weitzenböck connection on the SL(5) extended space reproduces the exceptional field theory action, and its irreducible parts are exactly the M-theory and IIB geometric and non-geometr...
M-theory and Type IIB from a Duality Manifest Action
hep-th 2013-11 conditional novelty 6.0 of 10

Two inequivalent solutions of the SL(5) section condition reduce the same duality-manifest action to a four-dimensional M-theory truncation and a three-dimensional type IIB truncation.
Covariant action for a string in doubled yet gauged spacetime
hep-th 2013-07 accept novelty 6.0 of 10

The coordinate gauge symmetry of doubled spacetime is equivalent to the section condition, and a gauge connection built on this principle yields a string action covariant under all relevant symmetries, including for d...

Show 3 more citing papers

\beta-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework
hep-th 2013-06 conditional novelty 6.0 of 10

A ten-dimensional supergravity theory is built whose non-geometric Q-flux is identified with a connection coefficient, yielding a second curvature scalar and explicit equations of motion.
The O_{D,D} Geometry of String Theory
hep-th 2013-03 conditional novelty 6.0 of 10

The double field theory action equals a specific H-invariant contraction of the generalised torsion of a flat, metric-compatible Weitzenböck connection, reproducing the known action plus a previously ad hoc term.
The Geometry, Branes and Applications of Exceptional Field Theory
hep-th 2020-06 accept novelty 2.0 of 10

Exceptional field theory recasts the maximal supergravities as a single extended geometry whose local symmetry is the exceptional U-duality group Ed(d), with extra coordinates conjugate to brane winding modes.

How the literature uses it

23 arXiv papers cite this in 33 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 30 sentences without a confident label

Cites it as background 3 papers

Other interesting and relevant work on generalised geometry and double field theory can be found in [ref] .

The O_{D,D} Geometry of String Theory · Introduction · 1.00
Let us comment more on this issue.[See [ref] for more details on the generalised metric with the Lorentzian signature.]

Non-abelian U-duality at work · Spacetime signature · 0.93
For other related developments see also [ref] .

Subtracted Geometry from Harrison Transformations: II · Introduction and Summary · 0.99

What it cites · 49 sentences without a confident label

Contests 1 paper

The difficulties found in the examples in [ref] are now removed, forcing us instead to describe the dual solutions using a trivector for those cases.

U-duality in three and four dimensions · Introduction · contest 0.83

Builds on 1 paper

We can now repeat the analysis in [ref] including time amongst the dualisable coordinates in order to find the bosonic fields after the action of a duality.

U-duality in three and four dimensions · The transformation rules · 0.98

Uses the method or tool of 14 papers

We study the action of U-dualities by using generalised geometry [ref] which makes the duality symmetries of the supergravity manifest.

U-dual fluxes and Generalized Geometry · Introduction · 1.00
We study the action of U-dualities by using generalised geometry [ref] which makes the duality symmetries of the supergravity manifest.

Generalized Geometry and M theory · Introduction · 1.00
We study the action of U-dualities by using generalised geometry [ref] which makes the duality symmetries of the supergravity manifest.

SO(5,5) duality in M-theory and generalized geometry · Introduction · 1.00

Compares with 1 paper

This is the same result as obtained by Wick-rotations in [ref] and corresponds to a new extreme M2-brane of different tension and charge.

U-duality in three and four dimensions · $U_Ω$ acting on extreme M2-brane · 0.99

Cites as background 3 papers

More details can be found in [ref] .

U-duality in three and four dimensions · Spacelike dualities · 0.98
In particular, one may wonder what becomes of physical quantities such as mass and the 3-form charge when there is a non-zero trivector although progress has recently been made in understanding the geometry of the trivector in the context of string theory [ref] .

Non-Geometric Fluxes in Supergravity and Double Field Theory · Conclusions · 0.91
For a comprehensive review of the Kerr/CFT correspondence, see [ref] .

The Kerr/CFT correspondence and its extensions: a comprehensive review · $U_Ω$ acting on uncharged black M2-brane · 1.00

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