The geometry of D = 11 Killing spinors

By J. Gauntlett, Stathis Pakis. 2002

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We propose a way to classify the local form of all bosonic supersymmetric configurations of D = 11 supergravity, using the differential forms that can be constructed as bi-linears from the Killing spinors. We show that the most general bosonic geometries either have a privileged SU(5) or a (Spin(7)8) × structure, depending on whether the Killing vector constructed from the Killing spinor is timelike or null, respectively. In the time-like case we derive the general local form of the geometry and show that it is almost completely determined by a certain SU(5) structure on the ten-dimensional space orthogonal to the orbits of the Killing vector. We also deduce what further conditions must be imposed in order that the equations of motion are satisfied. We illustrate the formalism with some known solutions and also present some new solutions including a rotating generalisation of the resolved membrane solutions and generalisations of the recently constructed D = 11 Godel solution. We also prove some general vanishing theorems for compactifications with flux.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2a93a82dcb08a10937c18b96fba67fa01b8410fc

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Citations in the corpus

All supersymmetric solutions of minimal supergravity in five- dimensions (2002, methodology): “theories [1, 2 ] (for older work using techniques specific to four dimensions, see [3]).”
One Ring to Rule Them All ... and in the Darkness Bind Them (2004, background): “This was shown in [13] to be true whenever the Killing vector, (2.”
AdS 3 solutions of IIB supergravity from D3-branes (2005, background): “nsional solution. It is an established fact that a supersymmetric conﬁguration satisﬁes the classical ﬁeld equations provided the form-ﬁeld equations of motion and the Bianchi identities are satisﬁed [13]. The Bianchi identity dF= 0 is a consequence of supersymmetry as can be easily seen from Eq.(3.”
The spinorial geometry of supersymmetric backgrounds (2004, methodology): “At the other end, Gauntlett, Gutowski and Pakis have solved the Killing spinor equations of 11-dimensional supergravity in the presence of one Killing spinor [8, 9].”
Supersymmetric AdS5 solutions of M-theory (2004, methodology): “Note that in M-theory, the field equation for the 4-form receives higher-order gravitational corrections—in our conventions they can be found in the appendix of [20].”
Supergravity as generalised geometry II: Ed(d) × ℝ+ and M theory (2014, background): “1 Cliff(10, 1;R) For Cliff(10, 1;R) ≃ GL(32,R) ⊕ GL(32,R), following the conventions of [48] we take the representation with Γ((11)) = ΓΓ(1) .”
BPS Action and Superpotential for Heterotic String Compactifications with Fluxes (2003, background): “An educated guess for the superpotential(2), which we will argue (1)Group structures as a tool to classify and construct new solutions to supergravity and string theory were first used in [28] and then also in [29, 36, 37, 39, 42, 43, 46, 50] in connection with flux compactifications.”
Supersymmetric AdS(4) compactifications of IIA supergravity (2004, background): “There is already a considerable amount of literature on the subject, see [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34] for an inexhaustive list of references.”
Consistent supersymmetric Kaluza-Klein truncations with massive modes (2009, background): “Following the conventions of [34], by definition ǫ = e ∧ e(1) ∧ · · · ∧ e(10) and so vol(C8) = g 1 ∧ g(2) ∧ · · · ∧ g(8) .”
Lifshitz solutions of D=10 and D=11 supergravity (2010, background): “Note that in [30] JSU(5), ΩSU(5) were denoted by Ω, χ, respectively.”
G structures, fluxes and calibrations in M theory (2003, methodology): “Note also that this result holds for all cases where it is possible to construct an appropriate time-like Killing vector from the Killing spinors (not necessarily as a bilinear), and thus it holds in particular for the entire “time-like” class of [5].”
Four-dimensional SCFTs from M5-branes (2012, background): “This has been shown for other supergravity theories in [55, 56, 57], but has not been shown for the maximal gauged supergravity in seven dimensions.”
Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions (2007, methodology): “The general classes of supersymmetric solutions that we consider have been analysed using G-structure techniques [21, 22].”
M-theory, exceptional generalised geometry and superpotentials (2008, background): “These “integrability” conditions on the generalised geometry and EGG structures are the generalisations of the G-structure and intrinsic torsion classification of supersymmetric backgrounds [66].”