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#### Spinorial geometry and Killing spinor equations of 6-D supergravity

##### MPG-Autoren

AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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##### Volltexte (frei zugänglich)

1010.2632
(Preprint), 269KB

CQG_28_10_105001.pdf
(beliebiger Volltext), 325KB

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##### Zitation

Akyol, M., & Papadopoulos, G. (2011). Spinorial geometry and Killing spinor equations of 6-D supergravity. Classical and quantum gravity, 28(10): 105001. doi:10.1088/0264-9381/28/10/105001.

We solve the Killing spinor equations of 6-dimensional (1,0)-supergravity coupled to any number of tensor, vector and scalar multiplets in all cases. The isotropy groups of Killing spinors are $Sp(1)\cdot Sp(1)\ltimes \bH (1)$, $U(1)\cdot Sp(1)\ltimes \bH (2)$, $Sp(1)\ltimes \bH (3,4)$, $Sp(1) (2)$, $U(1) (4)$ and $\{1\} (8)$, where in parenthesis is the number of supersymmetries preserved in each case. If the isotropy group is non-compact, the spacetime admits a parallel null 1-form with respect to a connection with torsion the 3-form field strength of the gravitational multiplet. The associated vector field is Killing and the 3-form is determined in terms of the geometry of spacetime. The $Sp(1)\ltimes \bH$ case admits a descendant solution preserving 3 out of 4 supersymmetries due to the hyperini Killing spinor equation. If the isotropy group is compact, the spacetime admits a natural frame constructed from 1-form spinor bi-linears. In the $Sp(1)$ and U(1) cases, the spacetime admits 3 and 4 parallel 1-forms with respect to the connection with torsion, respectively. The associated vector fields are Killing and under some additional restrictions the spacetime is a principal bundle with fibre a Lorentzian Lie group. The conditions imposed by the Killing spinor equations on all other fields are also determined.