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Register a new userOn D=11 supertwistors, superparticle quantization and a hidden SO(16) symmetry of supergravity
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We consider a covariant quantization of the D=11 massless superparticle in the supertwistor framework. D=11 supertwistors are highly constrained, but the interpretation of their bosonic components as Lorentz harmonic variables and their momenta permits to develop a classical and quantum mechanics without much difficulties. A simple, heuristic `twistor quantization of the superparticle leads to the linearized D=11 supergravity multiplet. In the process, we observe hints of a hidden SO(16) symmetry of D=11 supergravity.
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We construct a new SO(3)$times$SO(3) invariant non-supersymmetric solution of the bosonic field equations of $D=11$ supergravity from the corresponding stationary point of maximal gauged $N=8$ supergravity by making use of the non-linear uplift formulae for the metric and the 3-form potential. The latter are crucial as this solution appears to be inaccessible to traditional techniques of solving Einsteins field equations, and is arguably the most complicated closed form solution of this type ever found. The solution is also a promising candidate for a stable non-supersymmetric solution of M-theory uplifted from gauged supergravity. The technique that we present here may be applied more generally to uplift other solutions of gauged supergravity.
We study the system of equations derived twenty five years ago by B. de Wit and the first author [Nucl. Phys. B281 (1987) 211] as conditions for the consistent truncation of eleven-dimensional supergravity on AdS_4 x S^7 to gauged N = 8 supergravity in four dimensions. By exploiting the E_7(7) symmetry, we determine the most general solution to this system at each point on the coset space E_7(7)/SU(8). We show that invariants of the general solution are given by the fluxes in eleven-dimensional supergravity. This allows us to both clarify the explicit non-linear ansatze for the fluxes given previously and to fill a gap in the original proof of the consistent truncation. These results are illustrated with several examples.
We formulate D=11 supergravity over the octonions by rewriting 32-component Majorana spinors as 4-component octonionic spinors. Dimensional reduction to D=4 and D=3 suggests an interpretation of the so-called dilaton vectors, which parameterise the couplings of the dilatons to other fields in the theory, as unit octavian integers - the octonionic analogues of integers. The parameterisation involves a novel use of the duality between points and lines on the Fano plane, and suggests a series of consistent truncations with N=8,4,2,1, giving the four curious supergravities studied by Duff and Ferrara
Extreme near-horizon geometries in D=11 supergravity preserving four supersymmetries are classified. It is shown that the Killing spinors fall into three possible orbits, corresponding to pairs of spinors defined on the spatial cross-sections of the horizon which have isotropy groups SU(3), G2, or SU(4). In each case, the conditions on the geometry and the 4-form flux are determined. The integrability conditions obtained from the Killing spinor equations are also investigated.
The relation between motion in $-1/r$ and $r^{2}$ potentials, known since Newton, can be demonstrated by the substitution $rrightarrow r^{2}$ in the classical/quantum radial equations of the Kepler/Hydrogen problems versus the harmonic oscillator. This suggests a duality-type relationship between these systems. However, when both radial and angular components of these systems are included the possibility of a true duality seems to be remote. Indeed, investigations that explored and generalized Newtons radial relation, including algebraic approaches based on noncompact groups such as SO(4,2), have never exhibited a full duality consistent with Newtons. On the other hand, 2T-physics predicts a host of dualities between pairs of a huge set of systems that includes Newtons two systems. These dualities take the form of rather complicated canonical transformations that relate the full phase spaces of these respective systems in all directions. In this paper we focus on Newtons case by imposing his radial relation to find an appropriate basis for 2T-physics dualities, and then construct the full duality. Using the techniques of 2T-physics, we discuss the hidden symmetry of the actions (beyond the symmetry of Hamiltonians) for the Hydrogen atom in $D$-dimensions and the harmonic oscillator in $bar{D}$ dimensions. The symmetries lead us to find the one-to-one relation between the quantum states, including angular degrees of freedom, for specific values of $left( D,bar{D}right) $, and construct the explicit quantum canonical transformation in those special cases. We find that the canonical transformation has itself a hidden gauge symmetry that is crucial for the respective phase spaces to be dual even when $D eqbar{D}$. In this way we display the surprising beautiful symmetry of the full duality that generalizes Newtons radial duality.
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