Spinorial geometry and Killing spinor equations of 6-D supergravity

Abstract

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.

34 pages, Minor changes

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• Supersymmetric Dyonic Strings in 6-Dimensions from 3-Dimensions
• The structure of all the supersymmetric solutions of ungauged N = (1,0),d=6 supergravity
• On the supersymmetric solutions of the Heterotic Superstring effective action
• Contact metric three manifolds and Lorentzian geometry with torsion in six-dimensional supergravity
• M-Horizons
• Topology and geometry of 6-dimensional (1,0) supergravity black hole horizons
• Twisted form hierarchies, Killing-Yano equations and supersymmetric backgrounds
• Real Killing Spinors in Neutral Signature
• From Static to Cosmological Solutions of N=2 Supergravity
• Brane solitons of (1,0) superconformal theories in six dimensions with hypermultiplets
• Classification of maximally supersymmetric backgrounds in supergravity theories
• $\epsilon$-contact structures and six-dimensional supergravity
• Spinorial geometry, horizons and superconformal symmetry in six dimensions