Vanishing scalar invariant spacetimes in supergravity

Coley, A. A.; Fuster, Andrea; Hervik, Sigbjørn; Pelavas, Nicos

doi:10.1088/1126-6708/2007/05/032

Cited by 25 publications

(67 citation statements)

References 34 publications

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“…In [22] it was shown that the higher-dimensional VSI spacetimes with fluxes and dilaton are solutions of type IIB supergravity. Exact VSI solutions of IIB supergravity with NS-NS and RR fluxes and dilaton have been constructed.…”

Section: Vanishing Curvature Invariants (Vsi)mentioning

confidence: 99%

“…Therefore, a necessary (but not sufficient) condition for a particular supergravity solution to preserve some supersymmetry is that the spacetime possess such a Killing vector. Therefore the supersymmetry properties of VSI type IIB supergravity solutions with a CCNV were studied [22]. Supersymmetry was also studied in the CSI-CCNV subclass of supergravity spacetimes [25].…”

Section: Vanishing Curvature Invariants (Vsi)mentioning

confidence: 99%

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Supersymmetry, holonomy and Kundt spacetimes

Brännlund

Coley

Hervik

2008

Class. Quantum Grav.

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Abstract. Supersymmetric solutions of supergravity theories, and consequently metrics with special holonomy, have played an important role in the development of string theory. We describe how a Lorentzian manifold is either completely reducible, and thus essentially known, or not completely reducible so that there exists a degenerate holonomy invariant lightlike subspace and consequently admits a covariantly constant or a recurrent null vector and belongs to the higher-dimensional Kundt class of spacetimes. These Kundt spacetimes (which contain the vanishing and constant curvature invariant spacetimes as special cases) are genuinely Lorentzian and have a number of interesting and unusual properties, which may lead to novel and fundamental physics.

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Section: Vanishing Curvature Invariants (Vsi)mentioning

confidence: 99%

Section: Vanishing Curvature Invariants (Vsi)mentioning

confidence: 99%

Supersymmetry, holonomy and Kundt spacetimes

Brännlund

Coley

Hervik

2008

Class. Quantum Grav.

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“…It has of course long been known that pp-waves with flat transverse space provide such backgrounds since all the scalar invariants vanish identically -recently the class of exact sugra solutions with vanishing scalar invariants was investigated in [1]-but they are exceptional.…”

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confidence: 99%

All-order consistency of 5D supergravity vacua

Meessen¹

2007

Phys. Rev. D

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We show that the maximally supersymmetric vacua of minimal d 5 N 1 sugra remain maximally supersymmetric solutions when taking into account higher order corrections.The question of whether a given supergravity solution is a consistent background for string propagation to all orders in perturbation theory is an interesting though hard one. It has of course long been known that pp-waves with flat transverse space provide such backgrounds since all the scalar invariants vanish identically -recently the class of exact sugra solutions with vanishing scalar invariants was investigated in [1]-but they are exceptional.A class of sugra solutions for which a proof of all-order consistency is highly desirable are the maximally supersymmetric solutions, and for most of them an answer is known: in Ref.[2], Kallosh and Rajaraman, by making use of superspace methods, showed the all-order consistency of aDS 2 S 2 in minimal N 2 d 4 sugra, of aDS 5 S 5 in type IIB, and also of aDS 4 S 7 and aDS 7 S 4 in Mtheory. Since the associated Minkowski and KowalskiGlikmann solutions [3][4][5] are pp-waves, we must conclude that all the maximally supersymmetric solutions in minimal N 2 d 4, type IIB-sugra or M-sugra are allorder consistent.The way Kallosh and Rajaraman attacked the problem leans heavily on the fact that the Riemann tensor and the field strengths are covariantly constant with respect to (w.r.t.) the Levi-Cività connection. This covariantly constancy, however, is due to the fact that the solutions describe symmetric spacetimes, G=H, with G-invariant field strengths. Interestingly, the vast majority of maximally supersymmetric solutions are described by symmetric spaces, and one can envisage similar arguments to apply for their consistency.The strange ducks in the pond are the maximally supersymmetric solutions in d 5 sugra [6 -10]. Solutions such as the near-horizon-BMPV solution or the Gödel space, are not symmetric [11]: rather, they describe homogeneous, naturally reductive spacetimes with compatible fluxes. As such, there is a metric compatible connection that parallelizes the Riemann tensor and the field strengths, but it is not the Levi-Cività one. We then should ask ourselves the question whether the maximally supersymmetric solutions of d 5 N 1 sugra are all-order exact or not, and how to attack the problem. The answer to the last question lies in the way one would construct, and indeed constructs, higher order sugra actions in lower dimensions, be they string inspired or not.Partial results have recently been obtained in Refs. [12 -14] and these works instigated the current investigations: the symmetric solution aDS 2 S 3 was shown to be maximally supersymmetric in Ref. [14] and aDS 3 S 2 in Ref.[13] in a theory with TrA^2 R corrections. This theory was constructed in [12] and they also derived the conditions for the existence of a maximally supersymmetric aDS 5 .Dealing with on-shell sypersymmetry in systems with higher orders is quite cumbersome: since it is on-shell, the supersymmetry transformations ''need to kn...

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“…Both the higher-dimensional VSI and CSI spacetimes are known to to admit solutions to supergravity theories [17,18]. Furthermore, the PP-wave spacetimes have been proven to be solutions to the vacuum equations of all gravitational theories with a Lagrangian constructed from SPIs [19].…”

Section: Introductionmentioning

confidence: 99%

Locally homogeneous Kundt triples and CSI metrics

Hervik

McNutt

2019

Class. Quantum Grav.

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A pseudo-Riemannian manifold is called CSI if all scalar polynomial invariants constructed from the curvature tensor and its covariant derivatives are constant. In the Lorentzian case, the CSI spacetimes have been studied extensively due to their application to gravity theories. It is conjectured that a CSI spacetime is either locally homogeneous or belongs to the subclass of degenerate Kundt metrics. Independent of this conjecture, any CSI spacetime can be related to a particular locally homogeneous degenerate Kundt metric sharing the same scalar polynomial curvature invariants. In this paper we will invariantly classify the entire subclass of locally homogeneous CSI Kundt spacetimes which are of alignment type D to all orders and show that any other CSI Kundt metric can be constructed from them.

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Vanishing scalar invariant spacetimes in supergravity

Abstract: Abstract. We show that the higher-dimensional vanishing scalar invariant (VSI) spacetimes with fluxes and dilaton are solutions of type IIB supergravity, and we argue that they are exact solutions in string theory. We also discuss the supersymmetry properties of VSI spacetimes.

Cited by 25 publications

References 34 publications

Supersymmetry, holonomy and Kundt spacetimes

Supersymmetry, holonomy and Kundt spacetimes

All-order consistency of 5D supergravity vacua

Locally homogeneous Kundt triples and CSI metrics

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