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キーワード:
High Energy Physics - Theory, hep-th
要旨:
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.
