Two-dimensional gravities and supergravities as integrable systems

Nicolai, Hermann

doi:10.1007/3-540-54978-1_12

Cited by 58 publications

(164 citation statements)

References 53 publications

(45 reference statements)

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“…the manifest rigid G-symmetry of the two-dimensional theory, to a hidden rigid symmetry under an infinite-dimensional groupG, which is known as the Geroch group [5,6]. Quantities depending on the spectral parameter can be interpreted as elements ofG or of its Lie algebrag.…”

Section: Jhep06(2017)123mentioning

confidence: 99%

“…of eleven-dimensional supergravity, this might hold clues for formulating the theory nonperturbatively, for example using hyperbolic affine Lie algebras [6], the infinite-dimensional Lie algebra E 11 [12], or tensor hierarchy algebras [13], which all can be viewed as extensions of the Lie algebra of the Geroch group. It will be interesting to investigate which role R-H problems might play in this context.…”

Section: Jhep06(2017)123mentioning

confidence: 99%

“…Since P is the projection of the right-invariant Maurer-Cartan form to exp p G/H, the resulting sigma model metric is 6) where P m is the pull-back to N of the projection P of the right-invariant Maurer-Cartan form to p. Alternatively, since Q can be interpreted as a H-connection one-form, we can use it to gauge a G sigma model to obtain a sigma model with target space G/H. The corresponding gauge connection Q m is obtained by pulling back the connection form Q to N .…”

Section: Jhep06(2017)123mentioning

confidence: 99%

“…(6.4) 6 We note that demanding analyticity in τ = ±i does not constitute a significant restriction, in general.…”

Section: Canonical Factorization Yields Solution Of Equations Of Motionmentioning

confidence: 99%

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A Riemann-Hilbert approach to rotating attractors

Câmara¹,

Cardoso²,

Mohaupt³

et al. 2017

J. High Energ. Phys.

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We construct rotating extremal black hole and attractor solutions in gravity theories by solving a Riemann-Hilbert problem associated with the Breitenlohner-Maison linear system. By employing a vectorial Riemann-Hilbert factorization method we explicitly factorize the corresponding monodromy matrices, which have second order poles in the spectral parameter. In the underrotating case we identify elements of the Geroch group which implement Harrison-type transformations which map the attractor geometries to interpolating rotating black hole solutions. The factorization method we use yields an explicit solution to the linear system, from which we do not only obtain the spacetime solution, but also an explicit expression for the master potential encoding the potentials of the infinitely many conserved currents which make this sector of gravity integrable.

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Section: Jhep06(2017)123mentioning

confidence: 99%

Section: Jhep06(2017)123mentioning

confidence: 99%

Section: Jhep06(2017)123mentioning

confidence: 99%

“…(6.4) 6 We note that demanding analyticity in τ = ±i does not constitute a significant restriction, in general.…”

Section: Canonical Factorization Yields Solution Of Equations Of Motionmentioning

confidence: 99%

See 2 more Smart Citations

A Riemann-Hilbert approach to rotating attractors

Câmara¹,

Cardoso²,

Mohaupt³

et al. 2017

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…The linear equations, referred to as the Breitenlohner-Maison (BM) linear system [12,23] 12) can be viewed as the generalisation of the relation ∂ ± V V −1 = P ± + Q ± for the Lie algebravalued expression ∂ ± V V −1 , in light of the Lie algebra decomposition under the symmetric space automorphism. The integrability condition…”

Section: Two-dimensional Reduction and Bm Linear Systemmentioning

confidence: 99%

An inverse scattering formalism for STU supergravity

Katsimpouri

Kleinschmidt

Virmani

2014

J. High Energ. Phys.

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STU supergravity becomes an integrable system for solutions that effectively only depend on two variables. This class of solutions includes the Kerr solution and its charged generalizations that have been studied in the literature. We here present an inverse scattering method that allows to systematically construct solutions of this integrable system. The method is similar to the one of Belinski and Zakharov for pure gravity but uses a different linear system due to Breitenlohner and Maison and here requires some technical modifications. We illustrate this method by constructing a four-charge rotating solution from flat space. A generalization to other set-ups is also discussed.

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Gauged supergravities in various spacetime dimensions

Weidner

2007

Fortschritte der Physik

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In this review articel we study the gaugings of extended supergravity theories in various space-time dimensions. These theories describe the low-energy limit of non-trivial string compactifications. For each theory under consideration we review all possible gaugings that are compatible with supersymmetry. They are parameterized by the so-called embedding tensor which is a group theoretical object that has to satisfy certain representation constraints. This embedding tensor determines all couplings in the gauged theory that are necessary to preserve gauge invariance and supersymmetry. The concept of the embedding tensor and the general structure of the gauged supergravities are explained in detail. The methods are then applied to the half-maximal (N = 4) supergravities in d = 4 and d = 5 and to the maximal supergravities in d = 2 and d = 7. Examples of particular gaugings are given. Whenever possible, the higher-dimensional origin of these theories is identified and it is shown how the compactification parameters like fluxes and torsion are contained in the embedding tensor.

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Two-dimensional gravities and supergravities as integrable systems

Cited by 58 publications

References 53 publications

A Riemann-Hilbert approach to rotating attractors

A Riemann-Hilbert approach to rotating attractors

An inverse scattering formalism for STU supergravity

Gauged supergravities in various spacetime dimensions

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