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Generalised U-dual solutions in supergravity
High Energy Physics - Theory · Submitted 3 Mar 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate a method to take solutions of type IIA supergravity on a 3-sphere, with NSNS flux, to new solutions of 11-dimensional supergravity, using exceptional geometry techniques.
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The abstract, sentence by sentence
We discuss the notion of generalised U-duality as a solution generating technique in supergravity. We demonstrate a method to take solutions of type IIA supergravity on a 3-sphere, with NSNS flux, to new solutions of 11-dimensional supergravity, using exceptional geometry techniques. These new solutions are characterised by an underlying 3-algebra structure, and generalise features of solutions obtained by non-abelian T-duality, which involve an underlying ordinary Lie algebra. We focus on an example where we start with the pp-F1-NS5 solution in type IIA supergravity. We discuss the properties of our resulting new solution, including the possibility of viewing it globally as a U-fold, and its M2 and M5 brane charges. In the extremal case, the new solution admits an AdS${}_3$ limit, which falls into a recently constructed class of M-theory AdS$_{3}$ backgrounds -- this provides a global completion of our solution with a well-defined holographic dual, similar to the global completions of non-abelian T-dual solutions. Our full solution is a 6-vector deformation of this AdS${}_3$ limit. We also explicitly solve the Killing spinor equation in the AdS${}_3$ limit, finding a $\frac{1}{2}$-BPS solution.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss the notion of generalised U-duality as a solution generating technique in supergravity. | background 0.60 | 0.65 | 0.09 | asserted 0.81 |
| s1 | We demonstrate a method to take solutions of type IIA supergravity on a 3-sphere, with NSNS flux, to new solutions of 11-dimensional supergravity, using exceptional geometry techniques. | method 0.62 | 0.95 | 0.24 | asserted 1.00 |
| s2 | These new solutions are characterised by an underlying 3-algebra structure, and generalise features of solutions obtained by non-abelian T-duality, which involve an underlying ordinary Lie algebra. | result 0.56 | 0.73 | 0.24 | asserted 1.00 |
| s3 | We focus on an example where we start with the pp-F1-NS5 solution in type IIA supergravity. | method 0.62 | 0.86 | 0.03 | asserted 0.97 |
| s4 | We discuss the properties of our resulting new solution, including the possibility of viewing it globally as a U-fold, and its M2 and M5 brane charges. | contribution 0.45 | 0.92 | 0.12 | hedged possibility 0.79 |
| s5 | In the extremal case, the new solution admits an AdS${}_3$ limit, which falls into a recently constructed class of M-theory AdS$_{3}$ backgrounds -- this provides a global completion of our solution with a well-defined holographic dual, similar to the global completions of non-abelian T-dual solutions. | result 0.61 | 0.67 | 0.23 | asserted 0.91 |
| s6 | Our full solution is a 6-vector deformation of this AdS${}_3$ limit. | result 0.85 | 0.90 | 0.11 | asserted 1.00 |
| s7 | We also explicitly solve the Killing spinor equation in the AdS${}_3$ limit, finding a $\frac{1}{2}$-BPS solution. | result 0.85 | 0.97 | 0.10 | asserted 1.00 |
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The paper
Original abstract
We discuss the notion of generalised U-duality as a solution generating technique in supergravity. We demonstrate a method to take solutions of type IIA supergravity on a 3-sphere, with NSNS flux, to new solutions of 11-dimensional supergravity, using exceptional geometry techniques. These new solutions are characterised by an underlying 3-algebra structure, and generalise features of solutions obtained by non-abelian T-duality, which involve an underlying ordinary Lie algebra. We focus on an example where we start with the pp-F1-NS5 solution in type IIA supergravity. We discuss the properties of our resulting new solution, including the possibility of viewing it globally as a U-fold, and its M2 and M5 brane charges. In the extremal case, the new solution admits an AdS${}_3$ limit, which falls into a recently constructed class of M-theory AdS$_{3}$ backgrounds -- this provides a global completion of our solution with a well-defined holographic dual, similar to the global completions of non-abelian T-dual solutions. Our full solution is a 6-vector deformation of this AdS${}_3$ limit. We also explicitly solve the Killing spinor equation in the AdS${}_3$ limit, finding a $\frac{1}{2}$-BPS solution.
Human review
How the literature uses it
7 arXiv papers cite this in 45 sentences
Papers citing it · 30 sentences without a confident label
Builds on it 2 papers
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In this paper, I developed further the generalised U-duality transformation [ref], previously investigated in [ref] , mapping solutions of type IIA on $S^3$ to new 11-dimensional solutions.
Non-isometric U-dualities · Discussion · 0.96
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In other words, we are applying electromagnetic duality to the entirety of our previous generalised U-duality described in [ref] .
Generalised U-dual solutions via ISO(7) gauged supergravity · The initial D2 brane solution · 0.89
Uses its method or tool 2 papers
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Then (in principle) new solutions of 11-dimensional supergravity are constructed (locally) on the right-hand side by uplifting using the alternative consistent truncation described in [ref] .
Non-isometric U-dualities · Introduction · 0.83
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The Killing spinor equation we need to solve is[We follow the conventions we used in [ref] , in particular ${ Γ_a , Γ_b } = 2 η_ab$ with $η_ab$ having mostly minus signature.] [equation] where the Greek indices are the curved coordinates, and Latin indices are the flat ones.
Generalised U-dual solutions via ISO(7) gauged supergravity · SUSY analysis · 0.96
Compares with it 1 paper
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We further highlight the algebraic interpretation of the second consistent truncation, by concretely connecting it to the EDA proposal with accompanying $n$-algebra structure, and by comparison to our previous papers [ref] we demonstrate how this all fits into the pattern of generalised dualities naturally extending non-abelian T-duality of a three-sphere.
Generalised U-dual solutions via ISO(7) gauged supergravity · Introduction · 0.88
Cites it as background 2 papers
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Recently, a $U$-duality extension of the Drinfel'd double, called the Exceptional Drinfel'd Algebra (EDA), has been proposed in [ref] and various aspects of the EDA have been studied in [ref] .
Gauged sigma models and exceptional dressing cosets · Introduction · 0.99
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What is dubbed $𝐐$-flux here has recently been of considerable interest in the context of non-abelian U-duality, exceptional Drinfeld algebras and the construction of new uplifts to lower dimensional to 11-dimensional supergravity recently [ref] .
On exceptional QP-manifolds · Towards differential graded manifolds from Leibniz algebras · 0.97
What it cites · 100 sentences without a confident label
Builds on 3 papers
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For the $CSO(4,0,1)$ supergravity, numerous solutions were found in [ref] , all of which can be used to generate dual solutions by uplifting to type IIA on $S^3$ and to 11-dimensional supergravity via our EDA generalised frame.
Supersymmetric domain walls in 7D maximal gauged supergravity · Discussion · 0.84
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For the $CSO(4,0,1)$ supergravity, numerous solutions were found in [ref] , all of which can be used to generate dual solutions by uplifting to type IIA on $S^3$ and to 11-dimensional supergravity via our EDA generalised frame.
Supersymmetric solutions of 7D maximal gauged supergravity · Discussion · 0.84
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For the $CSO(4,0,1)$ supergravity, numerous solutions were found in [ref] , all of which can be used to generate dual solutions by uplifting to type IIA on $S^3$ and to 11-dimensional supergravity via our EDA generalised frame.
Twisted compactifications of 6D field theories from maximal 7D gauged supergravity · Discussion · 0.84
Uses the method or tool of 7 papers
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Having mapped our solution to seven-dimensional gauged supergravity, we now uplift it to a different higher-dimensional solution using a distinct consistent truncation corresponding to the exceptional Drinfeld algebra realisation of the $CSO(4,0,1)$ algebra [ref] .
Exploring Exceptional Drinfeld Geometries · 11-dimensional uplift via exceptional field theory · 0.97
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Here we need to introduce $μ^a$, $a=1,…,4$ as constrained coordinates on the $S^3$, $δ_ab μ^a μ^b= 1$, a unit determinant symmetric matrix[Note that what we call $M_ab$ is denoted $M^-1_αβ$ in [ref] .] $M_ab$ with inverse $M^ab$, and define [equation] Then the ansatz is [equation] where $D μ^a ≡dμ^a + g A_(1)^ab μ^b$, $D M^ab = d M^ab + 2 g A_(1)^(a|c M^c|b)$ and $F_(2)^ab = d A_(1)^ab +g A_(1)^ac ∧A_(1)^cb$.
S^3 and S^4 Reductions of Type IIA Supergravity · $CSO(4,0,1)$ from IIA on $S^3$ · 0.94
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This gives a solution generating mechanism, whereby type IIA solutions of this form can be consistently truncated to solutions of the seven-dimensional $CSO(4,0,1)$ gauged supergravity, and then uplifted to new solutions of 11-dimensional supergravity using the generalised geometric formulation of [ref] .
U-duality extension of Drinfel'd double · Introduction · 0.94
Compares with 6 papers
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Meanwhile the relationship between the M2 and M5 charges matches that following from equations (3.6) to (3.8) of [ref] .
$M$-strings and AdS$_3$ solutions to M-theory with small $\mathcal{N}=(0,4)$ supersymmetry · Charge quantisation · 0.98
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Hence the full factor $ϵ_AdS$ is [equation] Expanding the $r$ exponent, this can be seen to match the form of the AdS solutions obtained in [ref] .
A Construction of Killing Spinors on S^n · Supersymmetry · 0.91
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We can rewrite [ref] as [equation] Subtracting $1/3$ ([ref]) from ([ref]) we get: [equation] This (for suitable $β$) will provide a coordinate-dependent projector condition on $ϵ$, similar to that appearing in non-abelian T-dual solutions [ref] .
On non-abelian T-dual geometries with Ramond fluxes · Supersymmetry · 0.85
Cites as background 11 papers
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A proposal was made in [ref] for the algebra and generalised frames which should describe a notion of Poisson-Lie U-duality.
Poisson-Lie U-duality in Exceptional Field Theory · Poisson-Lie T- and Poisson-Lie U-duality · 0.86
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A proposal was made in [ref] for the algebra and generalised frames which should describe a notion of Poisson-Lie U-duality.
U-duality extension of Drinfel'd double · Poisson-Lie T- and Poisson-Lie U-duality · 0.86
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Exceptional field theory (see the review [ref] ) describes 11-dimensional supergravity backgrounds after splitting into a $d$-dimensional internal part, with coordinates $x^i$, and $(11-d)$-dimensional external part, with coordinates $X^μ$.
The Geometry, Branes and Applications of Exceptional Field Theory · Exceptional field theory dictionary · 0.98
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